t 



ELEMENTS 



OF 



ASTRONOMY. 



DESIGNED FOR 



ACADEMIES AND HIGH SCHOOLS. 



BY ELIaS LOOMIS, LL.D., 

PROFESSOR OF NATURAL PHILOSOPHY AND ASTRONOMY IN YALE COLLEGE, AND 
AUTHOR OF A "COURSE OF MATHEMATICS." 




*" I 



NEW YORK: 



HARPER & BROTHERS, PUBLISHERS, 
327 to 335 PEARL STREET. 



1897- 




/ 



K' 



LOOMIS'S SERIES OF TEXT-BOOKS. 



ELEMENTS OF ARITHMETIC. 28 cents. 

ARITHMETIC. 88 cents. 

TREATISE ON ALGEBRA. $1 00. 

GEOMETRY, CONIC SECTIONS, AND PLANE TRIGONOMETRY. $1 00. 

ELEMENTS OF TRIGONOMETRY, SURVEYING, AND NAVIGATION. $1 00. 

TABLES OF LOGARITHMS. $1 00. 

TRIGONOMETRY AND LOGARITHMS, bound in one volume. $1 50. 

ELEMENTS OF ANALYTICAL GEOMETRY. $1 00. 

DIFFERENTIAL AND INTEGRAL CALCULUS. $1 00. 

ANALYTICAL GEOMETRY AND CALCULUS, bound in one volume. $1 75. 

ELEMENTS OF ASTRONOMY. $1 00. 

PRACTICAL ASTRONOMY. $1 50. 

TREATISE ON ASTRONOMY. $150. 

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Published by HARPER & BROTHERS, New York. 



Entered, according to Act of Congress, in the year 1869, by 

Harper & Brothers, 

In the Clerk's Office of the District Court of the United States for the 
Southern District of New York. 



Copyright, 1897, by Henry B. Loomis and Francis E. Loomis. 



PREFACE. 



The plan of the present volume is essentially the same 
as that of my Treatise on Astronomy, with the omission 
of most of the mathematical portions. That which I have 
retained requires only a knowledge of a few of the most 
elementary principles of Algebra, Geometry, and Plane 
Trigonometry ; and without some mathematical knowl- 
edge, it is impossible to acquire an adequate idea of the 
substantial basis upon which the conclusions of Astronomy 
rest. If, however, a student is unable to understand the 
very simple mathematical portions of this volume, the de- 
scriptive part will generally be intelligible without them ; 
and the portions which it would be found necessary to 
omit would not, in the aggregate, much exceed twenty 
pages. Great care has been taken to render every state- 
ment clear and precise, and it is important that the stu- 
dent, in his recitations, should be trained to a similar pre- 
cision. 

Astronomers are now generally agreed that the value 
of the solar parallax, which has been for many years uni- 
versally accepted, is too small, but they are not agreed 
as to the precise value of this element which should be 
adopted. The value 8 /r .9, which I have employed in this 
work, is very nearly the mean of the values adopted by 
the most competent astronomers, and it is not probable 
that future observations mil require any great change in 
the value of this important element. 



CONTENTS. 



CHAPTER I. 

THE EARTH — ITS FIGURE, DIMENSIONS, AND DENSITY. — ROTATION. 

Page 

The Phenomena of the Diurnal Motion 9 

The Figure of the Earth — how determined 15 

Dimensions of the Earth — how determined 17 

The Celestial and Terrestrial Spheres 21 

Effects of Centrifugal Force upon the Form of the Earth 26 

Measurement of an Arc of the Meridian 28 

The Density of the Earth — how determined 32 

Direct Proof of the Earth's Rotation 35 

Artificial Globes— Problems on the Terrestrial Globe 37 

CHAPTER II. 

THE PRINCIPAL ASTRONOMICAL INSTRUMENTS. 

The Astronomical Clock — its Error and Rate 41 

The Transit Instrument — its Adjustments 42 

The Mural Circle — Reading Microscope 47 

The Altitude and Azimuth Instrument 51 

The Sextant — its Adjustments and Use 52 

CHAPTER III. 

ATMOSPHERIC REFRACTION. — TWILIGHT. 

The Law of Atmospheric Refraction 55 

Refraction determined by Observation 56 

The Cause of Twilight — its Duration 59 

CHAPTER IV. 

EARTH'S ANNUAL MOTION. — EQUATION OF TIME. — PARALLAX. 

The Sun's apparent Motion — the Equinoxes, Solstices, etc 62 

The Change of Seasons — its Cause G(> 

The Form of the Earth's Orbit 69 

Sidereal and Solar Time — Mean Time and Apparent Time 72 



VI CONTENTS. 

The Equation of Time explained 74 

How to find the Time at any Place 76 

The Calendar — Julian and Gregorian 79 

Diurnal Parallax — Horizontal Parallax 80 

Problems on the Terrestrial Globe 82 

Problems on the Celestial Globe 86 

CHAPTER V. 

THE SUN — ITS PHYSICAL CONSTITUTION. 

Distance and Diameter of the Sun 89 

The Physical Constitution of the Sun 90 

Appearance and Motion of the Solar Spots 92 

Theory of the Constitution of the Sun.. 97 

The Zodiacal Light described 99 

CHAPTER VI. 

ABERRATION. — PRECESSION OF THE EQUINOXES. — NUTATION. 

Aberration of Light — its Cause 101 

Precession of the Equinoxes — its Cause 103 

Nutation, Solar and Lunar 105 

CHAPTER VII. 

THE MOON — ITS MOTION — PHASES — TELESCOPIC APPEARANCE. 

Distance, Diameter, etc., of the Moon 107 

Phases of the Moon — Harvest Moon 110 

Telescopic appearance of the Moon 114 

Has the Moon an Atmosphere? 116 

The Moon's Mountain Forms 117 

CHAPTER VIII. 

CENTRAL FORCES. — GRAVITATION. 

Curvilinear Motion — Kepler's Laws 121 

The Law of Gravitation — Motions of Projectiles 123 

CHAPTER IX. 

ECLIPSES OF THE MOON. — ECLIPSES OF THE SUN. 

Dimensions, etc. , of the Earth's Shadow 129 

The Earth's Penumbra — its Dimensions 131 

Dimensions, etc., of the Moon's Shadow 133 

Different Kinds of Eclipses of the Sun 135 

Phenomena attending Eclipses of the Sun 136 

Rose-colored Protuberances — their Nature 137 



CONTENTS. Vll 

CHAPTER X. 

METHODS OF FINDING THE LONGITUDE OF A PLACE. 

Pac« 

Method by Chronometers explained U(j 

Method by Eclipses — Lunar and Solar HI 

Method by the Electric Telegraph — Transits of Stars 142 

CHAPTER XI. 

THE TIDES. 

Definitions — Cause of the Tides , 145 

Velocity of the Tidal Wave ,„.. 149 

The Tides modified by the Conformation of the Coast ,.. 150 

The Diurnal Inequality in the Height of the Tides 151 

Tides of the Gulf of Mexico — of the Coast of Europe 152 

CHAPTER XII. 

THE PLANETS THEIR APPARENT MOTIONS. 

Number of the Planets — their Orbits 154 

The apparent Motions of the Planets explained 156 

The Elements of the Orbit of a Planet 160 

To determine the Distance of a Planet from the Sun 1G2 

CHAPTER XIII. 

THE INFERIOR PLANETS. 

Greatest Elongations of the Planets — Phases „. 165 

Mercury — its Period, Distance, Diameter, etc 166 

Venus — its Period, Distance, Diameter, etc 167 

Transits of Mercury and Venus across the Sun's Disc 169 

Sun's Parallax — how determined ,.. 170 

CHAPTER XIV. 

THE SUPERIOR PLANETS. 

Mars — Period — Distance — Phases — Appearance , 1 72 

The Minor Planets — Discovery — Number, etc 174 

Jupiter — Distance — Diameter — Rotation, etc 176 

Jupiter's Satellites — Distances — Eclipses, etc 178 

Velocity of Light — how determined 180 

Saturn — Period — Distance — Rotation 181 

Saturn's Rings — their Disappearance explained 182 

Saturn's Satellites — their Number, Distance, etc l&~i 

Uranus — Period — Diameter — Satellites 18G 

Neptune — Discovery — Period — Satellite 1S1 



Vlll CONTENTS. 

CHAPTER XV. 

COMETS. — COMETARY ORBITS. — SHOOTING STARS. 

Pag« 

Number of Comets — the Coma — Nucleus — Tail, etc 189 

The Nebulous Envelope — its Dimensions and Changes 191 

The Tail — its rapid Formation — Dimensions, etc 193 

Halley's Comet — Encke's Comet — indications of a resisting Medium... 199 

Biela's Comet — Faye's Comet — Brorsen's Comet, etc 202 

Comet of 1744— Comet of 1770— Comet of 1813, etc 205 

Shooting Stars— Detonating Meteors — Aerolites 208 

CHAPTER XVI. 

THE FIXED STARS — THEIR DISTANCE AND THEIR MOTIONS. — NEBULAE. 

Classification of the Fixed Stars — their Brightness 215 

The Constellations — how Stars are designated 217 

Periodic Stars — Temporary Stars — Periodicity explained 220 

Distance of the Fixed Stars — Parallaxes determined 222 

Proper Motion of the Stars — Motion of the Solar System 225 

Double Stars — Color of the Stars — Stars optically Double 227 

Binary Stars — Periods — Masses, etc 229 

Clusters of Stars — Nebulae 232 

Classification of Nebulae — Variable Nebulae 234 

The Milky Way— its Constitution and Extent 240 

The Nebular Hypothesis — Conclusions from Geological Phenomena .*, 241 
Phenomena explained by this Hypothesis — Apparent Anomalies ex- 
plained 243 

How the Nebular Hypothesis maybe tested 244 






ASTKONOMY. 



CHAPTER I. 

GENERAL PHENOMENA OF THE HEAYEXS. — FIGURE OF THE 
EARTH. — ITS DIMENSIONS AND DENSITY. — PROOF OF ITS 
ROTATION. ARTIFICIAL GLOBES. 

1. Astronomy is the science which treats of the heavenly 
bodies. The heavenly bodies consist of the sun, the planets 
with their satellites, the comets with numerous meteoric 
bodies, and the fixed stars. 

Astronomy is divided into spherical and physical. Spher- 
ical Astronomy treats of the appearances, magnitudes, mo- 
tions, and distances of the heavenly bodies, together with 
the theory of the methods of observation and calculation by 
which the positions of the heavenly bodies are determined. 
That portion of Astronomy which treats chiefly of the di- 
rect results of observation, without explaining the calcula- 
tions by which the motions of the heavenly bodies are de- 
termined, is often called Descriptive Astronomy. That por- 
tion of Astronomy which treats chiefly of astronomical in- 
struments and astronomical observations, together with the 
solution of those practical problems which arise in the course 
of those observations, is often called Practical Astronomy. 

Physical Astronomy investigates the cause of the motions 
of the heavenly bodies, and, by tracing the consequences of 
the law of universal gravitation, enables us to follow the 
movements of the heavenly bodies through immense periods 
of time, either past or future. 

2. Diurnal Motion of the Heavens. — If we examine the 
heavens on a clear night, we shall soon perceive that the 
stars constantly maintain the same position relative to each 
other. A map showing the relative position of these bodies 



10 ASTRONOMY. 

on any night will represent them with equal exactness on 
any other night. They all seem to be at the same distance 
from us, and to be attached to the surface of a vast hemi- 
sphere, of which the place of the observer is the centre. 
But, although the stars are relatively fixed, the hemisphere, 
as a whole, is in constant motion. Stars rise obliquely from 
the horizon in the east, cross the meridian, and descend 
obliquely to the west. The whole celestial vault appears to 
be in motion round a certain axis, carrying with it all the 
objects visible upon it, without disturbing their relative po- 
sitions. The point of the heavens which lies at the extrem- 
ity of this axis of rotation is fixed, and is called the pole. 
There is a star called the pole star, distant about lj degrees 
from the pole, which moves in a small circle round the pole 
as a centre. All other stars appear also to be carried around 
the pole in circles, preserving always the same distance 
from it, 

3. Determination of the Axis of the Celestial Sphere. — Let 
the telescope of a theodolite, having a small magnifying 
power, be directed to the pole star ; the star will be found 
to move in a small circle, whose diameter is about three de- 
grees ; and the telescope may be so pointed that the star 
will move in a circle around the intersection of the spider 
lines as a centre. The point marked by the intersection of 
these lines is, then, the true position of the pole. The sur- 
face of the visible heavens, to which all the heavenly bodies 
appear to be attached, is called the Celestial Sphere. 

4. Use of a Telescope mounted Equatorially . — Having de- 
termined the axis of the celestial sphere, a telescope may be 
mounted so as to revolve upon a fixed axis which points to- 
ward the celestial pole in such a manner that the telescope 
may be placed at any desired angle with the axis, and there 
may be attached to it a graduated circle, by which the mag- 
nitude of this angle may be measured. A telescope thus 
mounted is called an equatorial telescope, and it is frequent- 
ly connected with clock-work, which gives it a motion round 
the axis corresponding with the rotation of the celestial 
sphere. 



GENERAL PHENOMENA OF THE HEAVENS. 11 

5. Diurnal Paths of the Heavenly Bodies. — Let now the 
telescope be directed to any star so that it shall be seen in 
the centre of the field of view, and let the clock-work be 
connected with it so as to give it a perfectly uniform mo- 
tion of rotation from east to west. The star will follow the 
telescope, and the velocity of motion may be so adjusted 
that the star shall remain in the centre of the field of view 
from rising to setting, the telescope all the time maintain- 
ing the same angle with the axis of the heavens. The same 
will be true of every star to which the telescope is directed ; 
from which we conclude that all objects upon the firma- 
ment describe circles at right angles to its axis, each object 
always remaining at the same distance from the pole. The 
same observations prove that this movement of rotation of 
all the stars is perfectly uniform. 

6 1 Time of one Revolution of the Celestial Sphere. — If the 
telescope be detached from the clock-work, and, having been 
pointed upon a star, be left fixed in its position, and the ex- 
act time of the stars passing the central wire be noted, on 
the next night, at about the same hour, the star will again 
arrive upon the central w^ire. The time elapsed between 
these two observations will be found to be 23h. 56m. 4s. 
expressed in solar time. 

This, then, is the time in which the celestial sphere makes 
one revolution ; and this time is always the same, whatever 
be the star to which the telescope is directed. 

7. A Sidereal Day . — The time of one complete revolution 
of the firmament is called a sidereal day. This interval is 
divided into 24 sidereal hours, each hour into 60 minutes, 
and each minute into 60 seconds. 

Since the celestial sphere turns through 360° in 24 side- 
real hours, it turns through 15 degrees in one sidereal hour, 
and through one degree in four sidereal minutes. 

8, The Diurnal Motion is never Suspended. — With a tel- 
escope of considerable power all the brighter stars can be 
seen throughout the day, unless very near the sun ; and, by 
the method of observation already described, we find that 



12 ASTRONOMY. 

the same rotation is preserved during the day as during the 
night. 

All of the heavenly bodies, without exception, partake of 
this diurnal motion ; but the sun, the moon, the planets, 
and the comets appear also to have a motion of their own, 
by which they change their position among the stars from 
day to day. 

9, The Celestial Equator is the great circle in which a 
plane passing through the earth's centre, and perpendicular 
to the axis of the heavens, intersects the celestial sphere. 
The celestial equator is frequently called the equinoctial. 

10, If a plummet be freely suspended by a flexible line, 
and allowed to come to a state of rest, this line is called a 
vertical line. The point where this line, produced upward, 
meets the visible half of the celestial sphere, is called the 
zenith. The point w^here this line, produced downward, 
meets the invisible half of the celestial sphere, is called the 
nadir. 

Every plane which passes through a vertical line is called 
a vertical plane or a vertical circle. 

That vertical circle which passes through the celestial 
pole is called the meridian. The vertical circle which cross- 
es the meridian at right angles is called the prime vertical. 

11, A horizontal plane is a plane perpendicular to a ver- 
tical line. 

The sensible horizon of a place on the earth's surface is 
the circle in which a horizontal plane, passing through the 
place, cuts the celestial sphere. This plane, being tangent 
to the earth, separates the visible from the invisible portion 
of the heavens. 

The rational horizon is a circle parallel to the sensible 
horizon, whose plane passes through the earth's centre. On 
account of the distance of the fixed stars, these two planes 
intersect the celestial sphere sensibly in the same great 
circle. 

The meridian of a place cuts the horizon in the north and 
south points ; the prime vertical cuts the horizon in the east 



GENERAL PHENOMENA OF THE HEAVENS. 



13 



and west points. These four points are called the cardinal 
points. 

12. The altitude of a heavenly body is the arc of a verti- 
cal circle intercepted between the centre of the body and 
the horizon. The zenith distance of a heavenly body is the 
arc of a vertical circle intercepted between its centre and 
the zenith. The zenith distance is the complement of the 
altitude. 

The azimuth of a heavenly body is the arc of the horizon 
intercepted between the meridian and a vertical circle pass- 
ing through the centre of the body. Altitudes and azi- 
muths are measured in degrees, minutes, and seconds, and 
they enable us to define the position of any body in the 
heavens. 

The amplitude of a heavenly body at the time of its ris- 
ing is the arc of the horizon intercepted between the centre 
of the body and the east point. Its amplitude at the time 
of its setting is the arc of the horizon intercepted between 
the centre of the body and the west point. If the azimuth 
of a star at rising is N. 58° E., its amplitude will be E. 32° BT. 

13, Consequences of the Diurnal Motion. — If an observer 
could watch the entire apparent path of any star in the sky, 
he would see it describe a complete circle ; but as only half 
the celestial sphere is visible at one time, it is evident that 

a part of the diurnal 
path of a star may lie 
below the horizon and 
be invisible. Thus, in 
Fig. 1, let PR be the 
axis of rotation of the 
celestial sphere, and let 
NLSK be the horizon 
produced to intersect 
the sphere, and divid- 
ing it into two hemi- 
spheres. Also, let NS 
be the north and south 
line. If the parallel 



Fig. 1. 




14 ASTRONOMY. 

circles passing through A, C, E, and G be the apparent diur- 
nal paths of four stars, then it is evident that — 

1st. The star which describes the circle AB will never de- 
scend below the horizon. 

2d. The star which describes the circle GH will never rise 
above the horizon. 

3d. The star which describes the circle CD will be above 
the horizon while it moves through ICK, and below the ho- 
rizon while it moves through KDI. 

4th. The star which describes the circle EF will be above 
the horizon while it moves through the portion LEM, and 
below the horizon while it moves through the portion MFL. 

These stars are said to rise at I and L, and to set at K and 
M. They rise in the eastern part of the horizon, and set in 
the western. 

With the star C, the visible portion of its path ICK is 
greater than the invisible portion KDI ; while with the star 
E, the visible portion of its path LEM is less than the invis- 
ible portion MFL. 

It is evident that all stars which lie to the north of the 
equator will remain above the horizon for a longer period 
than below it ; while all stars south of the equator will re- 
main above the horizon for a shorter time than below it ; 
and stars situated in the plane of the equator will remain 
above the horizon and below it for equal periods of time. 

14. Culminations of the Heavenly Bodies. — Since the me- 
ridian cuts all the diurnal circles at right angles, the stars 
will attain their greatest altitude when in this circle ; and 
they are then said to culminate. Moreover, since the me- 
ridian bisects the portions of the diurnal circles which lie 
above the horizon, the stars will require the same length of 
time in passing from the eastern horizon to the meridian as 
in passing from the meridian to the western horizon. 

The circumpolar stars cross the meridian twice every day, 
once above the pole and once below it. These meridian pas- 
sages are called upper and lower culminations. Thus the 
star which describes the circle AB,Fig. l,has its upper cul- 
mination at A, and its lower culmination at B. 



GENERAL PHENOMENA OF THE HEAVENS. 15 

15. How the Pole Star may be found. — Among the most 
remarkable of the stars which never set in the latitude of 
New York is the group of seven stars known as the Dipper, 
in the constellation Ursa Major, shown on the left of Fig. 2, 

Fig. 2. 




which also represents the constellation Ursa Minor near the 
middle of the figure, and Cassiopea on the right. The two 
stars a and (3 of Ursa Major are sometimes called the Point- 
ers, because a straight line drawn through them and pro- 
duced will pass almost exactly through the pole star in 
Ursa Minor, and thus the pole star may always be identi- 
fied whenever the Pointers can be seen. 

16. What Stars never set. — If a circle were drawn through 
X,Fig. 1, the north point of the horizon, parallel to the equa- 
tor, it w x ould cut off a portion of the celestial sphere having 
P for its centre, all of which would be above the horizon ; 
and a circle drawn through S, the south point of the horizon 
parallel to the equator, would cut off a portion having P'for 
its centre, which would be wholly below the horizon. Stars 
which are nearer to the visible pole than the point N never 
set, while those which are nearer to the invisible pole than 
the point S never rise. 

17. Why a Knowledge of the Dimensions of the Earth is 
important. — The bodies of which Astronomy treats are all 
(with the exception of the earth) inaccessible. Hence, for 
determining their distances, w r e are obliged to employ indi- 
rect methods. The eye can only judge of the direction of 



16 ASTRONOMY. 

objects, and can not accurately estimate their distance, es* 
pecially if they are very remote ; but by measuring the 
bearings of an inaccessible object from two points whose 
distance from each other is known, we may compute the dis- 
tance of that object by the methods of trigonometry. In 
all our observations for determining the distance of the 
celestial bodies, the base line must be drawn upon the earth. 
It therefore becomes necessary to determine with the ut- 
most precision the form and dimensions of the earth. 

18. Proof that the Earth is Globular. — That the earth is 
a body of a globular form is proved by the following con- 
siderations : 

1st. Navigators have repeatedly sailed entirely round the 
earth. This fact can only be explained by supposing that 
the earth is rounded; but it does not alone furnish suffi- 
ciently precise information of its exact figure, particularly 
since, on account of the interposition of the continents, the 
path of the navigator is necessarily somewhat circuitous, 
and is limited to certain directions. 

2d. When a vessel is receding from the land, an observer 

Fig. 3. 




from the shore first loses sight of the hull, then of the lower 
part of the masts and sails, and lastly of the topmast. Now, 
if the sea were an indefinitely extended plane, the topmast, 
having the smallest dimensions, should disappear first, while 
the hull and sails, having the greatest dimensions, should 
disappear last ; but, in fact, the reverse takes place. If we 
suppose the surface of the sea to be rounded, the different 
parts of a receding ship should disappear as they pass suc- 
cessively below the line of sight AB, Fig. 4, which is tan- 




FIGUEE OF THE EARTH. 17 

Fig. 4. gent to the surface 

k jj& 4A1 B of the sea. So also 
land is often visible 
from the topmast 
when it can not be 
seen from the deck. An aeronaut, ascending in his balloon 
after sunset, has seen the sun reappear with all the effects 
of sunrise ; and on descending, he has witnessed a second 
sunset. 

3d. If we travel northward following a meridian, we shall 
find the altitude of the pole to increase continually at the 
rate of one degree for a distance of about 69 miles. This 
proves that a section of the earth made by a meridian plane 
is very nearly a circle, and also affords us the means of de- 
termining its dimensions, as shown in Arts. 20 and 21. 

4th. Eclipses of the moon are caused by the earth coming 
between the sun and moon, so as to cast its shadow upon 
the latter, and the form of this shadow is always such as 
one globe would project upon another. This argument is 
conclusive ; but, before it can be appreciated, it is necessary 
to understand many principles which will be explained in 
subsequent chapters. 

5th. The most accurate measurements made in the man- 
ner described in Arts. 38 to 41 not only prove that the 
earth is nearly globular, but also show 1- precisely how much 
it deviates from an exact sphere. 

19, First Method of determining the Earth "s Diameter. — 
The considerations just stated not only demonstrate that 
the earth is globular, but also afford us a rude method of 
computing its diameter. For this purpose we must meas- 
ure the height of some elevated object, as the summit of a 
mountain, and also the distance at which it can be seen at 
sea. Now it has been ascertained that one of the peaks of 
the Andes, which is four miles in height, can be seen from 
the ocean at the distance of 179 miles. Let BD, Fig. 5, rep- 
resent this mountain, and AB the distance at which it can 
be seen from the ocean, the line AB being supposed to be 
a tangent to the surface of the water at the point A. Then, 
since BAC is a right-angled triangle, we have bv Geom., 
Book IY. 5 Prop. IT. : 



18 



ASTRONOMY. 




CB 2 = CA 2 -fAB 2 . 

If we represent the radius of the earth 
by R, we shall have 

(R + 4) 2 =R 2 +179 2 , 
from which we find that R equals near- 
ly 4000 miles. 

It is immaterial from what direction 
the mountain is observed, or in what 
part of the world it is situated, we al- 
ways obtain by this method nearly the same value of the 
earth's radius, which proves that the curvature of the 
earth is nearly the same in all azimuths and in all latitudes, 
and demonstrates conclusively that the earth is nearly a 
sphere. 

20. Second Method of determining the Earth's Diameter. 
— Having ascertained the general form of the earth, it is 
important to determine its diameter as accurately as possi- 
ble. For this purpose we first ascertain the length of one 
Fig g. degree upon its surface — that is, the distance be- 
tween two points on the earth's surface so situ- 
ated that the lines drawn from them to the centre 
of the earth may make with each other an angle 
of one degree. 

Let P and P' be two places on the earth's sur- 
face distant from each other about 70 miles, and 
let C be the centre of the earth. Supj30se that 
two persons at the places P and P' observe two 
stars S and S', which are at the same instant ver- 
tically over the two places — that is, in the direc- 
tion of plumb-lines suspended at those places. 
Let the directions of these plumb-lines be con- 
tinued downward so as to intersect at C the 
centre of the earth. The angle which the direc- 
tions of these stars make at P is SPS', and the 
angle, as seen from C, is SCS' ; but, on account of the dis- 
tance of the stars, these angles are sensibly equal to each 
other. If, then, the angle SPS' be measured, and the dis- 
tance between the places P and P' be also measured by the 
ordinary methods of surveying, the length of one degree can 



pj/p' 



FIGURE OF THE EARTH. ID 

be computed. In this way it has been ascertained that the 
length of a degree of the earth's surface is about 69 statute 
miles, or about 365,000 feet. 

Since a second is the 3600th part of a degree, it follows 
that the length of one second upon the earth's surface is 
very nearly one hundred feet. 

Since the plumb-line is every where perpendicular to the 
earth's surface, two plumb-lines at different places can not 
be parallel to each other, but must be inclined at an angle 
depending upon their distance. This inclination may be 
found by allowing one second for every hundred feet, or 
more exactly by allowing 365,000 feet for each degree. 

21. The circumference of the earth maybe found approx- 
imately by the proportion 

1 degree : 360 degrees :: 69 miles : 24,840 miles, 
which differs but little from the most accurate determina- 
tion of the earth's circumference as stated in Art. 41. The 
diameter of the earth is hence determined to be a little over 
7900 miles. 

Since the earth is globular, it is evident that the terms up 
and doicn can not every where denote the same absolute 
direction. The term tip simply denotes from the earth's 
centre, while down denotes toward the earth's centre ; but 
the absolute direction denoted by up at New York is dia- 
metrically opposite to that w^hich is denoted by up in Aus- 
tralia. 

22. Irregularities of the EartKs Surface. — The highest 
mountain peaks slightly exceed five miles in height, which 
is about two °f the earth's diameter. Accordingly, on a 
globe 16 inches in diameter, the highest mountain peak 
w r ould be represented by a protuberance having an eleva- 
tion of -y^j inch, which is about twice the thickness of an 
ordinary sheet of writing-paper. The general elevation of 
the continents above the sea would be correctly represented 
by the thinnest film of varnish. Hence w r e conclude that 
the irregularities of the earth's surface are quite insignifi- 
cant w T hen compared with its absolute dimensions. ' 



20 ASTRONOMY. 

23. Cause of the Diurnal Motion of the Heavens. — The 
apparent diurnal rotation of the heavens was formerly ex- 
plained by admitting that the heavenly bodies do really re- 
volve about the earth once in 24 hours. But it will hereaft- 
er be shown conclusively that the fixed stars are material 
bodies of vast size, and situated at an immense distance 
from us ; and hence, if they really revolve about the earth 
once in 24 hours, they must move with a velocity exceeding 
a thousand millions of miles in a second. This rapid mo- 
tion in a circle would generate a centrifugal force well-nigh 
infinite, which could only be balanced by the attraction of a 
central body of enormous size. The earth is too insignifi- 
cant to produce the required effect, and hence this hypothe- 
sis is utterly inconsistent with the fundamental princijDles 
of Mechanics. 

The appearances which we have described may be per- 
fectly explained by supposing that the stars remain station- 
ary, and that the earth rotates upon an axis once in 24 
hours in a direction opposite to that in which the heavens 
seem to revolve. Such a rotation of the earth would give 
to the celestial sphere the appearance of revolving in the 
contrary direction, as the forward motion of a boat on a 
river gives to the banks an appearance of backward motion ; 
and, since the motion of the earth is perfectly uniform, we 
are insensible of it, and hence attribute the change in the 
situation of the stars with respect to the earth to an actual 
motion of the heavenly bodies. The apparent motion of 
the heavens being from east to west, the real rotation of the 
earth, which produces that appearance, must be from west 
to east. 

The hypothesis of the earth's rotation is rendered proba- 
ble by the analogy of the other members of our solar sys- 
tem. All the planets which we have been able satisfactori- 
ly to observe are found to rotate on their axes, and their 
figures are generally such as correspond to the time of their 
rotation. 

The doctrine of the earth's rotation does not, however, 
rest simply on probability or analogy, but is positively de- 
monstrated by several phenomena, which will be described 
in Arts. 42, 48, and 49. 



FIGURE OF THE EARTH. 21 

24. The earth's axis is the diameter around which it re- 
volves once a day. The extremities of this axis are the ter- 
restrial poles ; one is called the north pole, and the other the 
south pole. 

The terrestrial equator is a great circle of the earth per- 
pendicular to the earth's axis. 

Meridians of the earth are great circles passing through 
the poles of the earth. 

25. The latitude of a place is the arc of the meridian 
which is intercepted between that place and the equator. 
Latitude is reckoned north and south of the equator from 
to 90 degrees. 

A parallel of latitude is any small circle on the earth's 
surface parallel to the terrestrial equator. Every point of 
a parallel of latitude has the same latitude. These parallels 
diminish in size as we proceed from the equator toward 
either pole. 

The polar distance of a place is its distance from the near- 
est pole, and is the complement of the latitude. 

26. The longitude of a place is the arc of the equator in- 
tercepted between the meridian passing through that place 
and some assumed meridian, to which all others are refer- 
red. This assumed meridian is called the first meridian. 
Longitude is usually reckoned east and w T est of the first me- 
ridian from to 180 degrees. Sometimes it is reckoned 
from the first meridian westward entirely round the circle 
from to 360 degrees. 

Different nations have adopted different first meridians. 
The English reckon longitude from the Royal Observatory 
at Greenwich ; the French from the Imperial Observatory 
at Paris ; and the Germans from the Observatory at Berlin, 
or from the island of Ferro (the most westerly of the Ca- 
nary Islands), which is assumed to be 20 degrees west of the 
Observatory of Paris. In the United States we sometimes 
reckon longitude from Washington, and sometimes from 
Greenwich. 

The longitude and latitude of a place designate its posj 
tion on the earth's surface. 



22 



ASTRONOMY. 



27. The Altitude of the Pole.— Let S^ENQ represent the 
earth surrounded by the distant starry sphere HZOK. Since 
the diameter of the earth is insignificant in comparison with 
the distance of the stars, the appearance of the heavens will 
be the same whether they are viewed from the centre of the 
earth or from any point on its surface. Suppose the ob- 
server to be at P, a point on the surface between the equa- 
tor JE and the north pole N. The latitude of this place is 
iEP, or the angle JECF. If the line CP be continued to the 




firmament, it will pass through the point Z, which is the ze- 
nith of the observer. If the terrestrial axis NS be continued 
to the firmament, it will pass through the celestial poles N' 
and S'. If the terrestrial equator JEQ be continued to the 
heavens, it will constitute the celestial equator JE'Q'. The 
observer at P will see the entire hemisphere HZO, of which 
his zenith Z is the pole. The other hemisphere HKO will 
be concealed by the earth. 

The arc NO contains the same number of degrees asiE'Z, 
each being the complement of ZIST; that is, the altitude of the 
visible pole is every where equal to the latitude of the place. 
Also, the arc ZN' is the complement of ON' ; that is, the 



FIGURE OF THE EARTH. 23 

zenith distance of the visible pole is the complement of the 
latitude. 

It will be perceived that, in proceeding from the equator 
to the north pole, the altitude of the north pole of the heav- 
ens will gradually increase from to 90 degrees. This in- 
crease in the altitude of the pole is owing to the fact that in 
following the curved surface of the earth, the horizon, which 
is continually tangent to the earth's surface, becomes more 
and more depressed toward the north, while the absolute di- 
rection of the pole remains unchanged. 

If the spectator be in the southern hemisphere, the ele- 
vated pole will be the south pole. 

28. How the Latitude of a Place may he Determined. — If 
there were a star situated precisely at the pole, its altitude 
would be the latitude of the place. The pole star describes 
a small circle around the pole, and crosses the meridian 
twice in each revolution, once above and once below the 
pole. The half sum of the altitudes in these two positions 
is equal to the altitude of the pole — that is, to the latitude 
of the place. The same result would be obtained by observ- 
ing any circumpolar star on the meridian both above and 
below the pole. 

29. Circles which pass through the two poles of the celes- 
tial sphere are called celestial meridians or hour circles. If 
two such circles include an arc of 15 degrees of the celestial 
equator, the interval between the instants of their coinci- 
dence with the meridian of a particular j)lace will be one 
hour. 

30. The right ascension of a heavenly body is the arc of 
the celestial equator intercepted between a certain point on 
the equator called the vernal equinox, and the hour circle 
which passes through the centre of the body. Right ascen 
sion is sometimes expressed in degrees, minutes, and seconds 
of arc, but generally in hours, minutes, and seconds of time. 
It is reckoned eastward from zero up to 24 hours, or 360 
degrees. 

If the hands of the sidereal clock be set to Oh. 0m. 0s. when 



24 



ASTRONOMY. 



the vernal equinox is on the meridian, the clock (if it neither 
gains nor loses time) will afterward indicate at each instant 
the right ascension of any object which is then on the me- 
ridian, for the motion of the hands of the clock corresponds 
exactly with the apparent diurnal motion of the heavens. 
While 15 degrees of the equator are passing the meridian, 
the hands of the clock will move through one hour. 

The sidereal day, therefore, begins when the vernal equi- 
nox is on the meridian, and the sidereal clock should al- 
ways indicate Oh. Om. Os. when the vernal equinox is on the 
meridian. 




31. The declination of a heavenly body is its distance 
from the celestial equator measured upon the hour circle 
which passes through its centre. Declination is either north 
or south, according as the object is on the north or south 
side of the equator. North declination is generally regard- 
ed as positive, and south declination as negative. 

The position of an object on the firmament is designated 
by means of its right ascension and declination. 

The north polar distance of a star is its distance from the 
north pole, and is the complement of the declination. 

32. A Right Sphere.— The diur- 
nal motion of the heavenly bodies 
presents different appearances to 
observers in different latitudes. 
When the observer is situated at 
the terrestrial equator, both the 
celestial poles will be in his hori- 
zon, the celestial equator will be 
perpendicular to the plane of the 
horizon, and hence the horizon will 
bisect the equator and all circles parallel to it. The heav- 
enly bodies will appear to rise perpendicularly on the east- 
ern side of the horizon, and set perpendicularly on the west- 
ern side. Such a sphere is called a right sphere, because 
the circles of diurnal motion are at right angles to the hori- 
zon. 

Since the diurnal circles are bisected by the horizon, all 




FIGURE OF THE EARTH. 25 

tlie stars will remain for equal periods above and below the 
horizon. 

83. A Parallel Sphere. — If the observer were at one of 
Fi s- 9 - the poles of the earth, the celestial 

pole would be in his zenith, and there- 
fore the celestial equator would coin- 
cide with his horizon. By the diur- 
nal motion, the stars would move in 
circles parallel to the horizon, and the 
whole hemisphere on the side of the 
elevated pole would be continually 
visible, while the other hemisphere 
would always remain invisible. This 
is called a parallel sphere. In a parallel sphere, a star situ- 
ated upon the equator would be carried by the diurnal mo- 
tion round the horizon, without either rising or setting. 

34. An Oblique Sphere. — At all places between the equa- 
tor and the pole, the celestial equator is inclined to the hori- 
zon at an angle equal to the distance of the pole from the 
zenith — that is, equal to the complement of the latitude of 
the place. 

A parallel of declination, BO, Fig. 7, whose polar distance 
is equal to the latitude of the place, will lie entirely above 
the horizon, and just touch it at the north point. This cir- 
cle is called the circle of perpetual apparitioyi, because the 
stars which are included within it never set The radius of 
this circle is equal to the latitude of the place. 

The parallel of declination HL, whose distance from the 
invisible pole is equal to the latitude of the place, will be 
entirely below the horizon, and just touch it at the south 
point. This circle is called the circle of perpetual occulta- 
tion, because the stars which are included within it never 
rise. The radius of this circle is also equal to the latitude 
of the place. 

One half of the celestial equator will be above the horizon 
and the other half below it. Hence every star on the equa- 
tor will be above the horizon during as long a time as it is be- 
low, and will rise at the east point, and set at the west point. 

B 



26 ASTRONOMY. 

With the exception of the equator, all diurnal circles 
comprised between the circles of perpetual apparition and 
occupation will be divided unequally by the horizon. The 
greater part of the circle DF will be above the horizon, 
and the greater part of the circle GK will be below the ho- 
rizon ; that is, all stars between the celestial equator and 
the visible pole are longer above than below the horizon, 
while all stars on the other side of the equator are longer 
below than above the horizon. 

The celestial sphere here described is called an oblique 
sphere, because the circles of diurnal motion are oblique to 
the horizon. 

35. Effects of Centrifugal Force. — We have proved that 
the earth has a globular form, and that it rotates upon its 
axis once in 24 sidereal hours. But, since the earth rotates 
upon an axis, its form can not be that of a perfect sphere / 
for every body revolving in a circle acquires a centrifugal 
force which tends to make it recede from the centre of its 
motion. Thus a stone whirled round in a sling acquires 
a tendency to fly off in a straight line ; and when a sphere 
revolves on its axis, every particle not lying immediately 
upon the axis acquires a centrifugal force which increases 
Fig. 10. -kt with its distance from the axis. 

Let NJESQ,Fig. 10, represent 
>^ a sphere which revolves on an 
^p axis NS, and let P be any par- 
ticle of matter upon its sur- 
face, revolving in a circle whose 
radius is EP. This particle, by 
its motion in a circle, acquires 
a centrifugal force which acts 
in a direction EP perpendicu- 
lar to the axis of rotation. This centrifugal force, which 
we will represent by PA, may be resolved into two other 
forces PB and PD, one acting in the direction of a radius of 
the earth, and the other at right angles to this radius. The 
former force, being opposed to the earth's attraction, has 
the effect of diminishing the weight of the body; the latter, 
being directed toward the equator, tends to produce motion 
in the direction of the equator. 




FIGURE OF THE EARTH. 27 

The intensity of the centrifugal force increases with the 
radius of the circle described, and is therefore greatest at 
the equator. Moreover, the nearer the point is to the equa- 
tor, the more directly is the centrifugal force opposed to the 
weight of the body. 

The effects, therefore, produced by the rotation of the 
earth are — 

1st. All bodies decrease in weight in going from the pole 
to the equator; and, 

2d. All bodies which are free to move tend from the high- 
er latitudes toward the equator. 

By computation, we find that at the equator the centrifu- 
gal force of a body arising from the earth's rotation once in 
24 sidereal hours is -$^§ part of the weight ; and, since this 
force is directly opposed to gravity, the weight must sustain 
a loss of -5^ part. 

This loss of weight from centrifugal force is greatest at the 
equator, and diminishes as we proceed toward either pole. 

36. Effect of Centrifugal Force upon the Form of a Body. 
—We have seen that a portion of the centrifugal force rej> 
resented by PD, Fig. 10, causes a tendency to move toward 
the equator. If the surface of the sphere were entirely sol- 
id, this tendency would be counteracted by the cohesion of 
the particles. But a large portion of the earth's surface is 
liquid, and this portion must yield to the centrifugal force, 
and flow toward the equator. The water is thus made to 
recede from the higher latitudes in either hemisphere, and 
accumulate around the equator. Thus the earth, instead of 
being an exact sphere, assumes the form of an oblate sphe- 
roid, a solid having somewhat the figure of an orange. The 
amount of the deviation from an exact sphere depends upon 
the intensity of the centrifugal force, and the attraction ex- 
erted by the earth upon bodies placed on its surface. A 
sphere consisting of any plastic material, like soft clay, may 
be reduced to a spheroidal form by causing it to rotate rap- 
idly upon an axis. 

37. Weight at the Pole and Equator compared. — We have 
found that at the equator the loss of weight due to centrif 



28 



ASTRONOMY. 



ugal force is -^l^. From a comparison of observations of 
the length of the seconds' pendulum made in different parts 
of the globe, it is found that the weight of a body at the 
pole actually exceeds its weight at the equator by y^. 
The difference between the fractions y^ and -^-g- is ^j ; 
that is, the actual attraction exerted by the earth upon a 
body at the equator is less than at the pole by the 590th 
part of the whole weight. This difference results from the 
greater distance of the body at the equator from the centre 
of the earth. 



Fig. 11. 



38. How an Arc of a Meridian is 
measured. — Numerous arcs of the me- 
ridian have been measured for the pur- 
pose of accurately determining the fig- 
ure and dimensions of the earth. These 
arcs are measured in the following man- 
ner : 

A level spot of ground is selected, 
where a base line, AB, from five to ten 
miles in length, is measured with the ut- 
most precision. A third station, C, is se- 
lected, forming with the base line a tri- 
angle as nearly equilateral as is conve- 
F nient. The angles of this triangle are 
measured with a large theodolite, and 
the two remaining sides may then be 
computed. A fourth station, D, is now 
selected, forming, with two of the for- 
mer stations, a second triangle, in which 
all the angles are measured ; and, since 
one side is already known, the others 
may be computed. A fifth station, E, is 
then selected, forming a third triangle ; and thus we pro- 
ceed forming a series of triangles, following nearly the direc- 
tion of a meridian. 

The bearing of each side, that is, its inclination to the 
meridian line, must also be measured, and hence we can 
compute how much any station is north or south of any 
other, and hence we can determine the distance between the 




DIMENSIONS OF THE EARTH. 29 

parallels of latitude passing through the most northerly and 
southerly points. The latitude of these two stations must 
now be determined, whence we obtain the difference of lati- 
tude corresponding to the arc measured. We thus have the 

measure of an are of a meridian expressed in miles, and also 

in degrees, and hence, by a proportion, we may find the 
length of an are of one degree. 
This method is the most accurate known for determining 

the distance between tWO remote points on the earth's sur- 
face, because we may choose the most favorable site for 
measuring accurately the base line; and, after this, nothing 
is required but t ho measurement of angles, which can be 
done with much less labor and with much greater accuracy 
than the measurement of distances. 

39. Verification ofthi Work-. — In order to verify the en- 
tire work, a second base line is measured near the end of the 

: cries of triangles, and we compare its measured length with 

the length as computed from the first base, through the in- 
tervention of t lie series of triangles. 

In the survey of the coast of the United States, three base 

lines have keen measured cast of New York, the shortest be- 
ing a little more than five miles in length, and the longest 

more than ten miles, and the two extreme bases are distant 
from each other 430 miles in a direct line. In one instance 

the observed length of a base differs from its length, as de- 
duced from one of the other bases, by six inches; in no other 
Case does the discrepancy exceed thru inches. This coinci 
deuce proves that none but errors of extreme minuteness 

have been committed in the determination of the position 

Of the intermediate stations st retching from the city of New 

York to the eastern boundary of Maine. 

40. Results of Measurements. — Tn the manner here de- 
scribed, arcs of the meridian have been measured in nearly 
every country of Europe. These surveys form a connected 
chain of triangles, extending from the North Cape, in lat. 

70°40',t0 an island in the Mediterranean, in lat. as 42', An 
arc lias been measured in India extending from lat. 29 26' 
to lat. 8° 5'. An arc has been measured in South America 



so 



ASTRONOMY. 



extending from the equator to more than three degrees of 
north latitude. An arc of four degrees has also been meas- 
ured in South Africa. The operations for the survey of the 
coast of the United States will ultimately furnish several 
important arcs of a meridian, but these observations are not 
yet fully reduced. 

These measurements enable us to determine with great 
accuracy the length of a degree of latitude for the entire 
distance from the equator to the north pole. The results are : 
A degree at the equator =6 8. V02 miles, or 362,748 feet. 
" in latitude 45° = 69.048 " 364,572 " 

" at the pole =69.396 " 366,410 " 

Difference of equato- ) _ _ Q 694 « 3662 « 

rial and polar arc ) ~ 



41. Conclusion from these Results, — If the earth were an 
exact sphere, a terrestrial meridian would be a perfect cir- 
cle, and every part of it would have the same curvature ; 
that is, a degree of latitude would be every where the same. 
But we find that the length of a degree increases as we pro- 
ceed from the equator toward the poles, and the amount of 
this variation affords a measure of the departure of a me- 
ridian from the figure of a circle. 

A plumb-line must every where be perpendicular to the 
surface of tranquil water, and (since the earth is not a 
sphere) can not every where point exactly toward the earth's 
centre. Let A,B be two plumb-lines suspended on the same 
rig. 12. meridian near the equator, and 

at such a distance from each 
other as to be inclined at an 
angle of one degree. Let C 
and D be two other plumb- 
lines on a meridian near one 
of the poles, also making with 
each other an angle of one de- 
gree. The distance from A to B is found to be less than 
from C to D, whence we conclude that the meridian curves 
more rapidly near A than near C. The two plumb-lines A 
and B will therefore intersect at a distance less than the 
equatorial radius, and the plumb-lines C and D will inter* 




DIMENSIONS OF THE EARTH. 31 

sect at a distance greater than the polar radius ; but the 
difference is purposely exaggerated in the figure. If the 
figure were made an exact representation of a section of the 
earth, it could not be distinguished from a perfect circle. 

It is found that all the observations in every part of the 
world are very accurately represented by supposing a me- 
ridian of the earth to be an ellipse, of which the polar di- 
ameter is the minor axis. 

The equatorial diameter of this ellipse is 7926.708 miles. 

The diameter in latitude 45° " 7913.286 " 

The polar diameter " 7899.755 " 

Difference of equatorial and polar 



26.953 
diameter is 



. f. 

Thus we find that the equatorial diameter exceeds the 
polar diameter by -^^ of its length. This difference is call- 
ed the ellipticity of the earth. 

The circumference of the earth, measured upon a meridian, 
is 24,857.43 miles; or a quadrant from the equator to the 
north pole is 6214.357 miles. 

From measurements which have been made at right an- 
gles to the meridian, it appears that the equator and paral- 
lels of latitude are very nearly, if not exactly circles. Hence 
it appears that the form of the earth is that of an oblate sphe- 
roid, a solid which may be supposed to be generated by the 
revolution of a semi-ellipse about its minor axis. This con- 
clusion leaves out of account the mountains upon the earth's 
surface, and refers simply to the surface of the sea. 

42. Loss of Weight at the Equator explained. — It has 
been mathematically proved that a spheroid whose ellip- 
ticity is -2-^, and whose average density is double the den- 
sity at the surface (which is the case with the earth, Art. 
46), exerts an attraction upon a particle placed at its pole 
greater by -g^ part than the attraction upon a particle at 
its equator; and this we have seen (Art. 37) is the fraction 
which must be added to the loss of weight by centrifugal 
force to make up the total loss of weight at the equator, as 
shown by experiments with the seconds' pendulum. 

This coincidence may be regarded as demonstrating that 
the earth does rotate upon its axis once in 24 hours. 



32 



ASTK0N0MY. 



Fig. 13- 




43. Equatorial Protuberance. — If a 
sphere be conceived to be inscribed 
within the terrestrial spheroid, having 
the polar axis NS for its diameter, a 
spheroidal shell will be included be- 
tween its surface and that of the sphe- 
roid having a thickness AB of 13 miles 
at the equator, and becoming gradual- 
ly thinner toward the poles. This shell of protuberant mat- 
ter, by means of its attraction, gives rise to the precession 
of the equinoxes, as will be explained hereafter, Art. 177. 

44. The Density of the Earth. — Several methods have 
been employed for determining the average density of the 
earth. These methods are generally founded upon the 
principle of comparing the attraction which the earth ex- 
erts upon any object with the attraction which some other 
body, whose mass is known, exerts upon the same object. 

First Method. — By comparing the attraction of the earth 
with that of a small mountain. 

In 1774 Dr. Maskelyne determined the ratio of the mean 
density of the earth to that of a mountain in Scotland by 
ascertaining how much the local attraction of the mountain 
deflected a plumb-line from a vertical position. This moun- 
tain stands alone on an extensive plain, so that there are no 
other eminences in the vicinity to affect the plumb-line. 
Two stations were selected, one on its northern and the other 
on its southern side, and both nearly in the same meridian. 
A plumb-line attached to an instrument designed for meas- 
uring small zenith distances was 
set up at each of these stations, and 
the distance from the direction of 
the plumb-line to a certain star was 
measured at each station the in- 
stant the star was on the meridian. 
The difference between these dis- 
tances gave the angle formed by 
the two directions of the plumb- 
lines AE, CG. Were it not for the 
mountain, the plumb-lines would 



Fig. 14. 




DENSITY OF THE EARTH, 



33 



take the positions AB, CD ; and the angle which they would 
in that case form with each other is found by measuring the 
distance between the two stations, and allowing about one 
second for every hundred feet. 

The disturbance of the plumb-lines caused by the attrac- 
tion of the mountain was thus found to amount to 12". It 
was computed that if the mountain had been as dense as the 
interior of the earth, the disturbance would have been about 
21". Hence the ratio of the density of the mountain to that 
of the entire earth was that of 12 to 21. By numerous bor- 
ings, the mean density of the mountain was ascertained to 
be 2.75 times that of water. Hence the mean density of 
the earth was computed to be 4.95 times that of water. 

From similar observations made in 1855 near Edinburg, 
the mean density of the earth was computed to be 5.32. 

45. Second Method. — The mean density of the earth has 
been determined by comparing the attraction of the earth 
with that of a large ball of metal, by means of the torsion 
balance. 

In the year 1798, Cavendish compared the attraction of 
the earth with the attraction of two lead balls, each of which 
was one foot in diameter. The bodies uj)on which their at- 
traction was exerted were two leaden balls, A, B, each about 
^g. 15. two inches in diameter. They were 

attached to the ends of a slender 
wooden rod, CD, six feet in length, 
which was suj>ported at the centre 
by a fine wire, EF, 40 inches long. 
The balls, if left to themselves, will 
come to rest when the supporting 
wire is entirely free from torsion, but 
a very slight force is sufficient to 
turn it out of this plane. The posi- 
tion of the rod CD was accurately 
observed w^ith a fixed telescope. The 
larg-e balls were then brought near 
the small ones, but on opposite sides, 
so that the attraction of both balls 
might conspire to twist the wire in the same direction, when 

B2 




84 ASTRONOMY. 

It was found that the small balls were sensibly attracted by 
the larger ones, and the amount of this deflection was care- 
fully measured. The large balls were then moved to the 
other side of the small ones, when the rod was found to be 
deflected in the contrary direction, and the amount of this 
deflection was recorded. This experiment w^as repeated 
many times. 

These experiments furnish a measure of the attraction of 
the large balls for the small ones, and hence we can com- 
pute what would be their attraction if they were as large as 
the earth. But we know the attraction actually exerted by 
the earth upon the small balls, this attraction being meas- 
ured by their weight. Thus we know the attractive force 
of the earth compared with that of the lead balls ; and, since 
we know the density of the lead, we can compute the aver- 
age density of the earth. From these experiments Caven- 
dish concluded that the mean density of the earth was 5.45. 

A much more extensive series of experiments made with 
the greatest care in 1841 indicated the mean density of the 
earth to be 5.67, and this is regarded as the most reliable 
determination hitherto made. 

46. Comparative Density at the Surface and at the Centre. 
— The average density of the rocks found near the earth's 
surface is about 2.6, which is not quite half the average den- 
sity of the earth. Hence Ave conclude that the density of 
the earth goes on increasing from the surface to the centre, 
and at the centre it may have the density of iron, or per- 
haps even of gold. This increased density may be supposed 
to be the result of the pressure of the superincumbent mass 
sustained by bodies at great depths below the surface. 

47. Volume and Weight of the Earth. — Having deter- 
mined the dimensions of the earth, we can easily compute its 
volume, and we find it amounts to 

259,400 millions of cubic miles. 

Knowing the density of the earth, we can also compute 

its weight. A cubic foot of water weighs 62^ pounds; 

hence a cubic foot of a solid whose specific gravity is 5.67 

will weigh 354 pounds. If we multiply the number of cubio 



PROOF OF THE EARTH'S ROTATION. 35 

ftcr m the earth by 354, we shall have its weight expressed 
in pounds. We thus find the weight of the earth to be 

6,000,000,000,000,000,000,000 tons, 
or six sextillions of tons. 

This number must not be regarded as fanciful or conjec- 
tural, but as a legitimate deduction from the most accurate 
observations which have hitherto been made, liable, howev- 
er, to some slight alteration if more accurate observations 
should hereafter be obtained. 

48. Direct Proof of the EartKs Rotation. — A direct proof 
of the earth's rotation is derived from observations of a pen- 
dulum. If a heavy ball be suspended by a flexible wire 
from a fixed point, and the pendulum thus formed be made 
to vibrate, its vibrations will all be performed in the same 
plane. If, instead of being suspended from a fixed point, 
we give to the point of support a slow movement of rota- 
tion around a vertical axis, the plane of vibration will still 
remain unchanged. This may be proved by fastening the 
wire to a spindle placed vertically, and giving to the spin- 
dle a slow movement of rotation (say four or five revolu- 
tions per minute) round the vertical axis ; the ball will be 
seen to rotate on its axis, without, however, changing its 
plane of vibration. 

Suppose, then, a heavy ball to be suspended by a wire 
from a fixed point directly over the pole of the earth, and 
made to vibrate, these vibrations will continue to be made 
in the same invariable plane. But the earth meanwhile 
turns round at the rate of 15 degrees per hour; and, since 
the observer is unconscious of his own motion of rotation, 
it results that the plane of vibration of the pendulum ap- 
pears to revolve at the same rate in the opposite direction. 

If the pendulum be removed to the equator, and set vi- 
brating in the direction of a meridian, the plane of vibration 
will still remain unchanged ; and since, notwithstanding the 
earth's rotation, this plane always coincides with a meridian, 
the plane of vibration will appear fixed, and no motion of 
the plane will be observed. 

The apparent motion of the plane of vibration is zero at 
the equator, and 15 degrees per hour at the poles. In go« 



36 



ASTRONOMY. 



Fig. 16. 




ing from the equator to the pole, the apparent motion of the 
plane of rotation increases steadily with the latitude, and at 
New Haven amounts to about 10 degrees per hour. 

It is indispensable to the 
success of this experiment 
that the pendulum should 
commence oscillating with- 
out any lateral motion. For 
this purpose the pendulum 
is drawn out of the vertical 
position, and tied to a fixed 
object by a fine thread. 
When the ball is quite at 
rest the thread is burned, 
and the pendulum com- 
mences its vibrations. Ex- 
periments of this kind have 
been made at numerous 
places. 

When the experiment is 
performed with the great- 
est care, the observed rate 
of motion coincides very 
accurately with the com- 
puted rate, and this coincidence may be regarded as a direct 
proof that the earth makes one rotation upon its axis in 24 
sidereal hours. 

49. Second Proof of the EariKs Rotation. — A second proof 
of the earth's rotation is derived from the motion of falling 
bodies. If the earth had no rotation upon an axis, a heavy 
body let fall from any elevation would descend in the direc- 
tion of a vertical line. But, if the earth rotates on an axis, 
then, since the top of a tower describes a larger circle than 
the base, its easterly motion must be more rapid than that 
of the base. If a ball be dropped from the top of the tower, 
since it has already the easterly motion which belongs to the 
top of the tower, it will retain this easterly motion during 
its descent, and its deviation to the east of the vertical line 
will be nearly equal to the excess of the motion of the top 




ARTIFICIAL GLOBES. 



37 



of the tower above that of the base during the 
time of fall. 

Let AB represent a vertical tower, and AA' 
the space through which the point A would be 
carried by the earth's rotation in the time that a 
heavy body would descend through AB. A body 
let fall from the top of the tower will retain the 
horizontal velocity which it had at starting, and, 
when it reaches the earth's surface, will have 
moved over a horizontal space, BD, nearly equal 
to A^V. But the foot of the tower will have 
moved only through BB', so that the body will 
be found to the east of the tower by a space nearly equal 
to B'D. 

This space B'D, for an elevation of 500 feet in the latitude 
of iSTew Haven, is but a little over one inch, so that it must 
be impossible to detect this deviation except from experi- 
ments conducted with the greatest care, and from an eleva- 
tion of several hundred feet. 




50. Results of Experiments. — Repeated experiments have 
been made in Italy and Germany for the purpose of detect- 
ing the deviation of falling bodies from a vertical line. The 
most satisfactory experiments were made in a mine 520 feet 
deep, with metallic balls an inch and a half in diameter. 
According to the mean of over a hundred trials, the eastei v 
ly deviation was 1.12 inch, while the deviation computed 
by theory should have been 1.08 inch. These experiments 
must be regarded as proving that the earth does rotate 
upon an axis. 



ARTIFICIAL GLOBES. 

51. Artificial globes are either terrestrial or celestial. The 
former exhibits a miniature representation of the earth, the 
latter exhibits the relative position of the fixed stars. The 
mode of mounting is usually the same for both, and many of 
the circles drawn upon them are the same for both globes. 

An artificial globe is mounted on an axis which is support- 
ed by a brass ring, MM, designed to represent a meridian, 
and is called the brass meridian. This ring is supported in 




38 ASTRONOMY. 

a vertical position by a frame in such 
a manner that the axis of the globe 
can be inclined at any angle to the 
horizon. The brass meridian is grad- 
uated into degrees, which are num- 
bered from the equator toward either 
pole from to 90 degrees. 

The horizon is represented by a 
broad wooden ring, HH, placed hori- 
zontally, whose plane passes through 
the centre of the globe. It is also graduated into degrees, 
which are numbered in both directions from the north and 
south points toward the east and west, to denote azimuths ; 
and there is usually another set of numbers, which begin 
from the east and west points, to denote amplitudes. This 
wooden ring is called the wooden horizon. 

Upon the wooden horizon are commonly represented the 
signs of the ecliptic, with divisions into degrees, and also the 
months, and days of each month, so arranged as to show the 
sun's place in the ecliptic for every day of the year. 

On the terrestrial globe, hour circles are represented by 
great circles drawn through the poles of the equator; and on 
the celestial globe corresponding circles are drawn through 
the poles of the ecliptic, and small circles parallel to the 
ecliptic are drawn at intervals often degrees. These are for 
determining celestial latitude and longitude. The ecliptic, 
tropics, and polar circles are drawn upon the terrestrial 
globe, as well as upon the celestial. 

About the north pole is a small circle graduated so as to 
indicate hours of the day and minutes ; while a small in- 
dex, I, called the hour index, attached to the brass meridian, 
points to one of the divisions upon this hour circle. This in- 
dex can be moved so as to point to any part of the hour circle. 
There is usually a flexible strip of brass, equal in length 
to one quarter of the circumference of the globe, which is 
graduated into degrees, and may be applied to the surface 
of the globe so as to measure the distance between two 
places, or it may measure the altitude of any point above 
the wooden horizon. Hence it is usually called the quad- 
rant of altitude. 



ARTIFICIAL GLOBES. 



39 



PROBLEMS ON THE TERRESTRIAL GLOBE. 

52* To find the Latitude and Longitude of a given Place. 
—Turn the globe so as to bring the given place to the grad- 
uated side of the brass meridian ; then the degree of the 
meridian directly over the place will indicate the latitude, 
and the degree of the equator under the brass meridian will 
indicate the longitude east or west of the first meridian* 

Verify the following by the globe : 



Lat. 

Paris 49° N. 

New York 40f ° N. 



Long. 
2i°E. 
74° W. 



Lat. 
San Francisco... 371° N. 
Cape Horn 55|° S. 



Long. 
122J°W. 
67i° W. 



53. The Latitude and Longitude of a Place being given, 
to find the Place. — Bring the degree of longitude on the 
equator under the brass meridian, then under the given de- 
gree of latitude on the brass meridian will be found the 
place required. 

Examples. 

1. What place is in lat, 30° N. and long. 90° W. ? 

Ans. New Orleans. 

2. What place is in lat. 23 N°. and long. 113 E°. ? 

Ans. Canton. 

3. What place is in lat. 38° S. and long. 145° E.? 

Ans. Melbourne. 



54. To find the Distance from one Place to another on the 
Earth's Surface. — Place the quadrant of altitude so that its 
graduated edge may pass through both places, and the point 
marked may be on one of them. Then the point of the 
quadrant which is over the other place will show the dis- 
tance between the two places in degrees, which may be re- 
duced to miles by multiplying them by 69, because 69 miles 
make nearly one degree. 

Examples. 

1. Find the distance of Liverpool from New York. 

Ans. 3600 miles. 

2. Find the distance of Jeddo from San Francises Ans. 



40 ASTRONOMY. 

3. Find the distance of Melbourne from San Francisco, 

Ans. 

55. To find the Antipodes of a given Place. — Bring the 
given place to the wooden horizon, and the opposite point 
of the horizon will indicate the antipodes. The one place 
will be as far from the north point of the wooden horizon <is 
the other is from the south point. 

Examples. 

1. Find the antipodes of Cape Horn. Ans. Irkutsk. 

2. Find the antipodes of London. Ans. 

3. Find the antipodes of the Sandwich Islands. Ans. 

56. Given the Hour of the Dai/ at any Place, to find the 
Hour at any other Place. — Bring the place at which the 
time is given to the brass meridian, and set the hour index 
to the given time. Turn the globe till the other place conies 
to the meridian, and the index will point to the required 
time. 

Examples. 

1. When it is 10 A.M. in New York, what is the hour in. 
San Francisco ? Ans. 6| A.M. 

2. When it is 5 P.M. in London, what is the hour in "Nev9 
York? Ans. 

3. AYhen it is noon in Xew York, what is the hour at Can 
ton ? An&* 



THE ASTRONOMICAL CLOCK. 41 



CHAPTER II. 

'INSTRUMENTS FOR OBSERVATION. THE CLOCK.— TRANSIT 

INSTRUMENT. MURAL CIRCLE. ALTITUDE AND AZIMUTH 

INSTRUMENT. THE SEXTANT. 

57. Why Observations are chiefly made in the Meridian. — ■ 
Whenever circumstances allow an astronomer to select his 
own time of observation, almost all his observations of the 
heavenly bodies are made when they are upon the meridian, 
because a large instrument can be more accurately and per- 
manently adjusted to describe a verticcd plane than any plane 
oblique to the horizon ; and there is no other vertical plane 
which combines so many advantages as the meridian. The 
places of the heavenly bodies are most conveniently ex? 
pressed by right ascension and declination, and the right as- 
cension is simply the time of passing the meridian, as shown 
by a sidereal clock. Moreover, when a heavenly body is at 
its upper culmination, its refraction and parallax are the 
least possible, and in this positicn refraction and parallax 
do not affect the right ascension of the body, but simply its 
declination ; while for every position out of the meridian 
they affect both right ascension and declination. 

58. The Astronomical Clock. — The capital instruments of 
an astronomical observatory are the clock, the transit in- 
strument, and the mural circle. 

In a stationary observatory, a pendulum clock is used for 
measuring time. The pendulum should be so constructed 
that its length may not be affected by changes of tempera- 
ture ; and the clock should rest upon a stone pier having a 
firm foundation, and not connected with the floor of the ob- 
servatory. It should be so regulated that, if a star be ob- 
served upon the meridian at the instant when the hands 
point to Oh, Om. Os., they will point to Oh. Om. Os. when the 
same star is next seen on the meridian. This interval is 



42 ASTRONOMY. 

called a sidereal day, and is divided into 24 sidereal hours. 
If the pendulum were perfectly adjusted, it would make 
86,400 vibrations in the interval between two successive 
returns of the same star to the meridian. But no clock is 
perfect, and it therefore becomes necessary to determine its 
error and rate daily, and, in reducing our observations, to 
make an allowance for the error of the clock. 

The error of a sidereal clock at any instant is its difference 
from true sidereal time. The rate of a clock is the change 
of its error in 24 hours. Thus if, on the 8th of January, 
when Aldebaran passed the meridian, the clock was found 
to be 30.84s. slow, and on the 9th of January, when the 
same star passed the meridian, the clock was 31.66s. slow", 
the clock lost 0.82s. per day. In other words, the error of 
the clock, Jan. 9th, was —31.66s., and its daily rate —0.82s. 

The error of a clock is found from day to day by observ- 
ing the time of transit of some star whose place has been ac- 
curately determined, and comparing the observed time with 
the star's right ascension. Where great accuracy is re- 
quired, the transits of several standard stars should be ob- 
served. To facilitate these observations, the apparent places 
of over a hundred stars are given in the Nautical Almanac. 

59. The Transit Instrument. — Most of the observations 
of the heavenly bodies are made when they are upon the ce- 
lestial meridian, and in many cases the sole business of the 
observer is to determine the exact instant w x hen the object 
is brought to the meridian by the apparent diurnal motion 
of the firmament. The passage of a heavenly body over the 
meridian is called a transit, and an instrument mounted in 
such a manner as to enable an observer, supplied with a suit- 
able clock, to determine the exact time of transit, is called a 
transit instrument. 

60. Transit Instrument described. — A transit instrument 
consists of a telescope, TT, mounted upon an axis, AB, at 
right angles to the tube, which axis occupies a horizontal 
position, and points east and west. The tube of the tele- 
scope, when horizontal, will therefore be directed north and 
south ; and if the telescope be revolved on its axis through 



TRANSIT INSTRUMENT.- — SPIRIT LEVEL. 



43 



Fig. 19. 



180 degrees, the central line of the tube will move in the 
plane of the meridian, and may be directed to any point on 
the celestial meridian. 

A small transit instrument is usually mounted upon a solid 
stand of cast iron, which can 
be easily moved from place 
to place. A large transit in- 
strument is mounted upon 
two stone piers, P,P, Fig. 19, 
which should have a solid 
foundation, and should stand 
on an east and west line. On 
the top of each of the piers is 
secured a metallic support in 
the form of the letter Y? to 
receive the extremities of the 
axis of the telescope. At the 
left end of the axis there is 
a screw, by which the Y of 
that extremity may be raised 
or lowered a little, in order 
that the axis may be made 
perfectly horizontal. At the right end of the axis is a screw, 
by which the Y of that extremity may be moved backward 
or forward, so as to enable us to bring the telescope into 
the plane of the meridian. 




61. The Spirit Level. — When the transit instrument is 

properly adjusted, its axis will be horizontal, and directed 

due east and west. If the axis be not exactly horizontal, 

its deviation may be ascertained by placing upon it a spirit 

Kg> 20. level. This consists of a glass 

C_ D tube, AB, nearly filled with al- 

3 cohol or ether. The tube forms 
a portion of a ring having a 
very large radius, and when it is placed horizontally, with 
its convexity upward, the bubble, CD, will occupy the high- 
est position in the middle of its length. A graduated scale 
is attached to the tube, by which we may measure any de- 
viation of the bubble from the middle of the tube. 



44 



ASTRONOMY. 



To ascertain whether the axis of the telescope is horizon- 
tal, apply the level to it, and see if the bubble occupies the 
middle of the tube. If it does not, one end of the axis must 
be elevated or depressed by turning the screw which moves 
one of the Y' s m a vertical direction (Art. 60). The level 
must now be taken up, and reversed end for end, when the 
bubble should still occupy the middle of the tube. If it 
does not, it indicates that the two legs of the level are not 
of equal length,, and the error must be corrected by turning 
the adjusting screw of the spirit level. This operation of 
reversing the level must be repeated until the bubble rests 
in the middle of the tube in both positions of the level. 

62. The Reticle. — In order to furnish within the field of 
view of the telescope a fixed point of reference, a system of 
wires or fibres is attached to a frame, and secured in the fo- 
cus of the eye-glass of the telescope, so that when seen 
through the eye-glass they appear like fine lines drawn 
across the field of view. Such an apparatus is Fip 21< 
called a reticle. In a theodolite there are gen- 
erally two wires intersecting at right angles at 
the centre of the field of view, and dividing it 
into quadrants, as show r n in Fig. 21. 

In the focus of the eye-piece of the transit 

instrument is secured a small frame to 
which are attached several parallel and 
equidistant wires, crossed by one or two 
others at right angles, Fig. 22. The lat- 
ter should be made horizontal, when the 
former wires will of course be vertical. 
When the reticle and the telescope 
have been properly adjusted, the mid- 
dle wire, MN, will be in the plane of the 
meridian, and when an object is seen upon it, the object will 
be on the celestial meridian. 




Fi£. 2? 




63. Method of observing Transits. — The fixed stars appear 
in the telescope as bright points of light without sensible 
magnitude, and by the diurnal motion of the heavens a star 
is carried successively over each of the wires of the transit 



METHOD OF OBSERVING TRANSITS. 45 

instrument. The observer, just before the star enters the 
field of view, writes down the hour and minute indicated by 
the clock, and proceeds to count the seconds by listening to 
the beats of the clock, while his eye is looking through the 
telescope. He observes the instant at which the star crosses 
each of the wires, estimating the time to the nearest tenth 
of a second ; and by taking a mean of all these observations, 
he obtains with great precision the instant at which the star 
passed the middle wire, and this is regarded as the true time 
of the transit. The mean of the observations over several 
wires is considered more reliable than an observation over 
a single wire. 

During the day, the wires of the reticle are visible as fine 
black lines stretched across the field of view. At night they 
are rendered visible by a lamp, L, Fig. 19, whose light passes 
through a perforation in the axis of the transit instrument, 
and is reflected to the eye-glass by a mirror placed diago- 
nally at the junction of the axis and telescope. The field 
of view may thus be illumined more or less at pleasure. 

When we observe the sun or any object which has a sen- 
sible disk, the time of transit is the instant at which the cen- 
tre of the disk crosses the middle wire. This time is ob- 
tained by observing the instants at which the eastern and 
western edges of the disk touch each of the wires in succes- 
sion, and taking the mean of all the observations. When 
the visible disk is not circular, special methods of reduction 
are employed. 

64. The Electro-chronograph. — In many observatories it 
is now customary to employ the electric circuit to record 
transit observations. An electro-magnetic recording appa- 
ratus is connected with the pendulum of an astronomical 
clock in such a manner that the circuit is broken at each vi- 
bration of the pendulum, and the seconds of the clock are 
denoted by a series of equally distant breaks in a line traced 
upon a sheet of paper to which an equable motion is given 
by machinery. At the instant a star is seen to pass one of 
the wires of the transit, the observer presses his finger upon 
a key, and a break is made in one of the short lines repre- 
senting seconds, as shown at A, B, and C, in Fig. 23. In this 



46 ASTRONOMY. 

Fig. 23. 
A . B 



way observations can be made with much greater accuracy 
than by the old method, and a greater number of observe 
tions can be made in a given time. 

65. Mate of the Diurnal Motion, — Since the celestial 
sphere revolves at the rate of 15 degrees per hour, or 15 sec- 
onds of arc in one second of time, the space passed over be- 
tween two successive beats of the pendulum will be 15 sec- 
onds of arc. When the sun is on the equator, and its appa- 
rent diameter is 32 minutes of arc, the interval between the 
contacts of the east and west limbs with the middle wire of 
the transit instrument will be 2m. 8s. 

66. To adjust a Transit Instrument to the Meridian. — A 
transit instrument may be adjusted to describe the plane of 
the meridian by observations of the pole star. Direct the 
telescope to the pole star at the instant of its crossing the 
meridian, as near as the time can be ascertained ; the transit 
will then be nearly in the plane of the meridian. The pole 
star is on the meridian when it attains its greatest or least 
altitude. It is now desirable to set the clock to indicate si- 
dereal time, which may be done as follows : Having leveled 
the axis, turn the telescope to a star about to cross the me- 
ridian near the zenith. Since every vertical circle intersects 
the meridian at the zenith, a zenith star will cross the field 
of the telescope at the same time, whether the plane of the 
transit coincide with the meridian or not. At the moment 
when the star crosses the central wire, set the clock to the 
star's right ascension as given by the Nautical Almanac, and 
the clock will henceforth indicate nearly sidereal time. The 
times of the upper and lower culminations of the pole star 
will now be known pretty accurately. Observe the pole 
star at one of its culminations, following its motion until the 
clock indicates its right ascension, or its right ascension plus 
12 hours. By means of the azimuth screw bring the middle 
wire of the telescope to coincide with the star, and the ad- 
justment will be nearly complete. 



THE MURAL CIRCLE. 



47 



67. Final Verification. — The axis being supposed perfect- 
ly horizontal, if the middle wire of the telescope is exactly 
in the meridian, it will bisect the circle which the pole star 
describes round the pole in 24 sidereal hours. If, then, the 
interval between the upper and lower culminations is exactly 
equal to the interval between the lower and upper, the ad- 
justment is perfect. But if the time elapsed while the star 
is traversing the eastern semicircle is greater than that of 
traversing the western, the plane in which the telescope 
moves is westward of the true meridian on the north hori- 
zon, and vice versa if the western interval is greatest. This 
error of position must be corrected by turning the azimuth 
screw. The adjustment must then be verified by further 
observations until the instrument is fixed in the meridian 
with all attainable accuracy. 

68. The Mural Circle. — The mural circle is an instrument 
used to measure the altitude of a heavenly body at the in- 
stant when it crosses the 
meridian. It consists of 
a large graduated circle, 
aaaa, Fig. 24, firmly at- 
tached at right angles to a 
horizontal axis upon which 
it turns. This axis is sup- 
ported by a stone pier or 
wall, whose face is accu- 
rately adjusted to the 
plane of the meridian. To 
the circle is attached a tel- 
escope, MM, so that the en- 
tire instrument, including 
the telescope, turns in the 
plane of the meridian. The 
circle is divided into degrees, and subdivided into spaces of 
five minutes, and sometimes of two minutes, the divisions 
being; numbered from to 360 degrees round the entire cir- 
cle. The smallest spaces on the limb are further subdivided 
to single seconds, sometimes by a vernier, but generally by 
a reading microscope. 




4$ 



ASTRONOMY. 



69. The Vernier. — A vernier is a scale of small extent, 
graduated in such a manner that, being moved by the side 
of a fixed scale, we are enabled to measure minute portions 
of this scale. The length of this movable scale is equal to 
a certain number of parts of that to be subdivided ; but it is 
divided into parts either one more or one less than those of 
the primary scale taken for the length of the vernier. Thus, 
if a circle is graduated to sixths of a degree, or 10 minutes, 
and we wish to measure single minutes by the vernier, we 
take an arc equal to 9 divisions upon the limb, and divide it 
into 10 equal parts. Then each division of the vernier will 
be equal to -^ of a degree, while each division of the scale is 
•^§ of a degree ; that is, each space on the limb exceeds one 

upon the vernier by one 
minute. 

Thus, let AB represent 
a portion of the limb of 
a circle divided into de- 
grees and 10' spaces, and 
let V represent the ver- 
nier, which may be moved 
entirely round the circle, 
and having 10 of its divi- 
sions equal to 9 divisions 
of the circle ; that is, to 
f of a degree. Therefore one division of the circle exceeds 
one division of the vernier by -^ of a degree. Now, as the 
sixth division of the vernier (in the figure) coincides with a 
division of the circle, the fifth division of the vernier will be 
V beyond the nearest division of the circle; the fourth divi- 
sion, 2'; and the zero of the vernier will be 6 7 beyond the 
next lower division of the circle ; i. e., the zero of the vernier 
coincides with 64° 16' upon the circle. 

In order, therefore, to read an angle for any position of 
the vernier, we observe what division of the vernier coin- 
cides with a division of the circle. The number of this line 
from the zero point indicates the minutes which are to be 
added to the degrees and minutes taken from the graduated 
circle. 

By increasing the number of subdivisions of the vernier, 







THE READING MICROSCOPE. 49 

much smaller quantities than one minute may be measured. 
With a circle of 8 inches' radius, we may easily read angles 
to 10 seconds, and with a circle of 2 feet radius we may 
measure angles as small as 1 or 2 seconds. 

70. The Reading Microscope. — The reading microscope is 
a compound microscope firmly attached to the pier which 
supports the circle, and having in its focus cross-wires which 
are moved laterally by a fine-threaded micrometer screw. 
The figure on the right shows the field of view, with the 
magnified divisions of the circle as seen through the micro- 
scope. When the microscope is properly adjusted, the im- 
age of the divided limb and the micrometer wires are dis- 
tinctly visible together. If the circle is divided into spaces 
of 5', then five revolutions of the screw must exactly meas- 
ure one of these spaces. One revolution of the head of the 
screw will therefore carry the wires over a space of one min- 
ute. The circumference of Fio . ^ 

the circle attached to the 
head, M, is divided into 60 
equal parts, so that the mo- 
tion of the head through 
one of these divisions ad- 
vances the wires through a 
space of one second. There are six of these microscopes, A, 
B, C, D, E, F, placed at equal distances round the circle, Fig. 
24, and firmly attached to the pier. 

71. To determine the Horizontcd Point upon the Limb of 
the Circle. — Direct the telescope upon any star which is 
about crossing the meridian, and bring its image to coincide 
with the horizontal wire which passes through the centre of 
the field of the telescope. Then read the graduation by 
each of the fixed microscopes. On the next night, place a 
basin containing mercury in such a position that, by direct- 
ing the telescope of the circle toward it, the same star may 
be seen reflected from the surface of the mercury, and bring 
the reflected image to coincide with the horizontal wire of 
the telescope. Then read the graduation as before. Now, 
by a law of optics, the reflected image will appear as much 

C 




50 ASTKONOMY. 

depressed below the horizon as the star is elevated above it ; 
therefore half the sum of the two readings, at either of the 
microscopes, will be the reading at the same microscope 
when the telescope is horizontal. 

72. To measure the Altitude of a Heavenly Body. — Hav- 
ing determined the reading of each of the microscopes when 
the telescope is directed to the horizon, if we wish to meas- 
ure the altitude of a star, direct the telescope upon it so that 
it may be seen on the horizontal wire as the star passes the 
meridian, and read off the angle from the several micro- 
scopes. The difference between the last reading and the 
reading when the telescope is horizontal is the altitude re- 
quired. 

The zenith distance of a star is found by subtracting its 
altitude from 90°. 

To measure the altitude of the sun or any object which 
has a sensible disk, measure the altitude of the upper and 
lower limbs, and take half their sum for the altitude of the 
centre ; or measure the altitude of the lower limb, and add 
the apparent semi - diameter taken from the Nautical Al- 
manac. 

73. To determine the Declination of a Heavenly Body, — 
The pole star crosses the meridian above and below the pole 
at intervals of 12 hours sidereal time, and the true position 
of the pole is exactly midway between the two points where 
the star crosses the meridian ; therefore half the sum of the 
altitudes of these points will be the altitude of the pole itself. 

The altitude of the pole being determined, that of the 
equator is also known, since the equator is 90 degrees from 
the pole. 

Having determined the position of the celestial equator, 
the declination of any star is easily determined, since its 
declination is simply its distance from the equator. Art. 31 . 

74. The Meridian Circle. — Since the mural circle has a 
short axis, its position in the meridian is unstable, and there- 
fore it can not be relied upon to give the right ascension of 
stars with great accuracy. The meridian circle is a combi- 



ALTITUDE AND AZIMUTH INSTRUMENT. 



51 



nation of the transit instrument and mural circle, being sim- 
ply a transit instrument with a large graduated circle at- 
tached to its axis. It is sometimes called a transit circle, and 
is now in common use at most of the large observatories. 



75. Altitude and Azimuth Instrument. — This instrument 
has one graduated circle, E Fig# 27. 

F, confined to a horizontal 
plane; a second graduated 
circle, N, perpendicular to 
the former, and capable of 
being turned to any azi- 
muth ; and a telescope, MM, 
firmly fastened to the sec- 
ond circle, and turning with 
it about a horizontal axis. 
The appearance of the in- 
strument will be learned 
from Fig. 27. 

76. Adjustments of this 
Instrument. — Before com- 
mencing observations with 
this instrument, the horizon- 
tal circle must be leveled, 
and also the axis of the tele- 
scope. The meridional point 
on the azimuth circle is its 
reading when the telescope 
is pointed north or south, and may be determined by ob- 
serving a star at equal altitudes east and west of the me- 
ridian, and finding the point midway between the two ob- 
served azimuths. The horizontal point of the altitude circle 
is its reading when the axis of the telescope is horizontal, 
and may be found in the manner described for the mural 
circle, Art. 71. 

This instrument has the advantage over the meridian cir- 
cle in being able to determine the place of a star in any part 
of the visible heavens ; but we ordinarily prefer the place 
of a star to be given in right ascension and declination in- 




52 



ASTRONOMY. 



stead of altitude and azimuth, and to deduce the one from 
the other requires a laborious computation. Hence the al- 
titude and azimuth instrument is but little used for astro- 
nomical observations, except for special purposes, as, for ex- 
ample, to investigate the laws of refraction. 

77, The Sextant. — The sextant is much used at sea for 
the determination of latitude and longitude, and is also fre- 
quently useful on land when only portable instruments can 
be obtained. It has a triangular frame. ABC, made of brass, 
with a wooden handle, H. It has a graduated limb, AB, 
comprising 60 or 70 degrees of the circle, but it is graduated 
into 120 or more degrees, and each degree is divided into six 
equal parts of 10' each, while the vernier gives angles to 10". 
The divisions are also continued a short distance on the oth- 
er side of zero toward A, forming what is called the arc of 
excess. The microscope, M, is used to read off the divisions 
on the graduated limb. At I is a screw for clamping the 
index to the limb ; and D is a tangent screw for giving the 
index. CG, a small motion, and thus securing an accurate 
contact of the images. Attached to the index bar, CG, the 
silvered index glass, C, is fixed perpendicular to the plane 
of the instrument. To the frame at X is attached a second 
glass, called the horizon glass, the lower half of which only 
Pie 2- ^~\ ^ s silvered. This is 

also perpendicular to 
the plane of the in- 
strument, and is par- 
allel to the plane of 
the index glass. C, 
when the vernier is 
set to zero on the 
limb AB. 

The telescope, T, is 
supported in a ring, 
K ; and in the focus 
of the object glass 
are placed two wires 
parallel to each oth- 
er, and equidistant from the axis of the telescope. At E and 




DIP OF THE HORIZON. 53 

F are colored glasses of different shades, to diminish the in- 
tensity of the light when a bright object, as the sun, is ob- 
served. 

78. To measure the Distance between two Objects. — Hold 
the sextant in the right hand by the handle, so that its plane 
may pass through both objects. Point the telescope upon 
one of the objects, and with the left hand move the index 
until the reflected image of the other object is brought to 
the centre of the field of the telescope, into apparent contact 
with the object seen directly. The angle is then read off 
from the limb by the aid of the microscope. 

79. To measure the Altitude of a Heavenly Body. — For 
an artificial horizon, place a shallow vessel containing a 
small quantity of mercury in a position convenient for ob- 
servation. Measure the angle between the body and its im- 
age reflected from the mercury as if this image were a real 
object. Half this angle will be the altitude of the body. 

In obtaining the altitude of a body at sea, its altitude 
above the visible horizon is measured by bringing the re- 
flected image into contact with the horizon. 

80. Dip of the Horizon. — The visible horizon which we 
employ in measuring altitudes at sea is depressed below the 
true horizontal plane. 

Let AC represent the radius of the earth, AD the height 
of the eye above the level of the sea, E 
DH a horizontal plane passing through 
the place of the observer ; then HDB 
will represent the depression of the ho- 
rizon, and is commonly called the dip 
of the horizon. This angle may be com- 
puted as follows : 

The angle BDH is equal to the angle 
BCD ; and in the right-angled triangle 
BCD we know BC, the radius of the 
earth, and CD, the radius of the earth plus the height of the 
observer. Hence, by Trigonometry, w^e can compute the an- 
gle BCD. 




54 ASTRONOMY. 

For an elevation of 25 feet the dip of the horizon amounts 
to nearly five minutes, and for an elevation of 100 feet it 
amounts to nearly 10 minutes. For an elevation of 3000 
feet the dip amounts to about one degree, and for an eleva- 
tion of 12,000 feet it amounts to about two degrees. 



ATMOSPHERIC REFRACTION. 



55 



CHAPTER HI 

ATMOSPHERIC REFRACTION. — TWILIGHT. 

81, The air which surrounds the earth gradually decreases 
in density as we ascend from the surface. At the height of 4 
miles its density is only about half as great as at the earth's 
surface ; at the height of 8 miles, about one fourth as great ; 
at the height of 12 miles, about one eighth as great, and so 
on. From this law it follows that at the height of 50 miles 
its density must be extremely small, so as to be nearly or 
quite insensible to ordinary tests. The phenomena of shoot- 
ing stars and the Aurora Borealis, however, indicate that a 
very feeble atmosphere extends to a height of 500 miles. 

82. Path of a Pay of Light. — According to a law of op- 
tics, when a ray of light passes obliquely from a rarer to a 
denser medium, it is bent toward the perpendicular to the 
refracting surface. Hence the light which comes from a 
star to the earth is refracted toward a vertical line. We 
may conceive the atmosphere to consist of an infinite num- 
ber of strata increasing in density from the top downward. 

Let SA be a ray of light com- 
ing from a distant object, S, and 
falling obliquely upon the at- 
mospheric strata. The ray SA, 
passing into the first layer, will 
be deflected in the direction AB, 
toward a perpendicular to the 
surface MX. Passing into the 
next layer, it will be again de- 
flected in the direction BC, more 
toward the perpendicular ; and, 
passing through the lowest layer, it will be still more deflect- 
ed, and will enter the eye at D, in the direction of CD ; and 
since every object appears in the direction from which the 



Fig. 30. 




56 ASTROXOMY. 

visual ray enters the eye, the object S will be seen in the 
direction DS', instead of its true direction AS. 

Since the density of the earth's atmosphere increases grad- 
ually from its upper surface to the earth, the path of a ray 
of light from a heavenly body is not a broken line, as we 
have here supposed, but a curve line concave toward the 
earth. Since the density of the upper part of the atmos- 
phere is very small, the curve at first deviates very little 
from a straight line, but the deviation increases as the ray 
approaches the earth. Both the straight and curved parts 
of the ray lie in the same vertical plane, for this plane is per- 
pendicular to all the strata of the atmosphere, and therefore 
the ray will continue in this plane in passing from one stra- 
tum to another. The refraction of the atmosphere therefore 
makes a star appear to be nearer the zenith than it really is, 
but its azimuth remains unchanged. 

In the zenith the refraction is zero, since the ray of light 
falls perpendicularly upon all the strata of the atmosphere. 
The refraction increases with the zenith distance ; for, the 
greater the zenith distance of a star, the more obliquely do 
the rays from it fall upon the different strata, and therefore, 
according to the principles of optics, the greater is the re- 
fraction. The refraction of a star is therefore greatest at 
the horizon. 

83. How the Refraction may be determined by Observa- 
tion. — In latitudes greater than 45°, a star w T hich passes 
through the zenith of the place may also be observed when 
it passes the meridian below the pole. Let the polar dis- 
tance of such a star be measured both at the upper and low- 
er culminations. In the former case there will be no refrac- 
tion ; the difference between the two observed polar dis- 
tances will therefore be the amount of refraction for the al- 
titude at the lower culmination ; because, if there were no 
refraction, the apparent diurnal path of the star would be a 
circle, with the celestial pole for its centre. 

This method is strictly applicable only in latitudes great- 
er than 45°, and by observations at one station we can only 
determine the refraction corresponding to a single altitude ; 
but by combining observations at different stations from 




ATMOSPHERIC REFRACTION. 57 

latitude 45° to 70°, we may determine the refraction for any 
altitude from zero to 50 degrees. 

84. A general Method of determining Refraction. — When 
the latitude of a place and the polar distance of a star which 
passes the meridian near the zenith have been determined, 
the refraction may be found for all altitudes from observa- 
tions at a single station. 

In Fig. 31, let PZH represent the meridian of the place of 
observation, P the pole, Z the Fig# Zlm 

zenith, and S the true place 

of the star. Let ZS be a ver- f \ ^\p 

tical circle passing through 
the star, and PS an hour cir- 
cle passing through the star. 
Then, in the triangle ZPS, PZ H 
is the complement of the latitude, which is supposed to be 
known ; PS is the polar distance of the star, which is also 
known. If, then, we knew also the angle ZPS, we could 
compute ZS, which represents the true zenith distance of the 
star. The difference between the computed value of ZS and 
its observed value will be the refraction corresponding to 
this altitude. Now the angle ZPS is the angular distance 
of the star from the meridian, or the difference between the 
time when the star was at S and the time when it crosses 
the meridian. 

If we commence our observations when the star is near 
the horizon, and continue them at short intervals until it 
reaches the meridian, measuring the apparent altitude, and 
noting the time of observation by the clock, we may deter- 
mine the amount of refraction for all altitudes from zero to 
90 degrees. 

The average value of refraction at the horizon is about 
35', or a little more than half a degree ; at an altitude of 10° 
it is only 5'; at 25° it is 2'; at 45° it is 1'; at 62° it is only 
30"; and in the zenith it is zero. 

85. Corrections for Temperature and Pressure. — The 
amount of refraction at a given altitude is not always the 
same, but depends upon the temperature and the pressure 

C2 



58 ASTRONOMY. 

of the air. Tables have been constructed, partly from ob- 
servation and partly from theory, by which we may readily 
obtain the mean refraction for any altitude; and rules are 
given by which the proper correction may be made for the 
height of the barometer and thermometer. 

86. Effect of Refraction upon the Time of Sunrise. — Since 
refraction increases the altitudes of the heavenly bodies, it 
must accelerate their rising and retard their setting, and thus 
render them longer visible. The amount of refraction at the 
horizon is about 35'', which being a little more than the ap- 
parent diameters of the sun and moon, it follows that, when 
the lower limb of one of these bodies appears just to touch 
the horizon, if there were no refraction it would be wholly 
invisible. 

87. Effect of Refraction upon the Figure of the Surfs DisTc. 
— When the sun is near the horizon, the lower limb, having 
the least altitude, is most affected by refraction, and there- 
fore more elevated than the upper limb, and thus the verti- 
cal diameter is shortened, while the horizontal diameter re- 
mains sensibly the same. This effect is greatest near the 
horizon, because there the refraction changes most rapidly 
for a given change of altitude. The difference between the 
vertical and horizontal diameters may amount to one fifth 
of the whole diameter. The disk thus assumes an elliptical 
foi*m, with its longer axis horizontal. 

88. Enlargement of the Sun near the Horizon. — The appa- 
rent enlargement of the sun and moon near the horizon is 
not due to refraction, but is an illusion of the judgment. If 
we measure the apparent diameters of these bodies with any 
suitable instrument, we shall find that, when near the hori- 
zon, they subtend a less angle than when seen near the zen- 
ith. This is owing to their greater distance from us in the 
former instance than in the latter, as explained in Art. 127. 
It is, then, through an error of judgment that they seem to 
us larger near the horizon. 

Our judgment of the absolute magnitude of a body is based 
upon our estimate of its distance. If two objects at unequal 



TWILIGHT. 59 

distances subtend the same angle, the more distant one must 
be the larger. Now the sun and moon, when near the hori- 
zon, appear to us more distant than when they are high in 
the heavens. They seem more distant in the former posi- 
tion, partly from the number of intervening objects, and 
partly from their diminished brightness. When the moon 
is near the horizon a variety of intervening objects shows us 
that the distance of the moon must be considerable ; but 
when the moon is high up in the sky no such objects inter- 
vene, and the moon appears quite near. For the same rea- 
son, the vault of heaven does not present the appearance of 
a hemisphere, but appears flattened toward the zenith, and 
spread out at the horizon. 

Our estimate of the distance of objects is also influenced 
by their clearness or obscurity. Thus a distant mountain, 
seen through a perfectly clear atmosphere, appears much 
nearer than when seen through a hazy atmosphere. The 
disks of the sun and moon, when near the horizon, appear 
much less brilliant than they do when high up in the heav- 
ens, and on this account we assign to them a greater distance. 

89. Cause of Twilight. — After the sun has set, its rays 
continue for some time to illumine the upper strata of the 
air, and are thence reflected to the earth, producing consid- 
erable light. As the sun descends farther below the hori- 
zon, a less part of the visible atmosphere receives his direct 
light — less light is reflected to the surface of the earth — un- 
til at length all reflection ceases, and night begins. Before 
sunrise in the morning, the same phenomena are exhibited 
in the reverse order. The illumination thus produced is 
called the twilight. 

Let ABCD, Fig. 32, represent a portion of the earth's sur- 
face ; let EFGH be the limit of the atmosphere, or at least 
of that part which reflects light visibly ; and let SAH be a 
ray of light from the sun, just grazing the earth at A, and 
leaving the atmosphere at the point H. The point A is il- 
lumined by the whole reflective atmosphere HGFE. The 
point B, to which the sun has set, receives no direct solar 
light, nor any light reflected from that part of the atmos- 
phere which is below ALH ; but it receives a twilight from 



60 ASTRONOMY, 

the portion HLF, which lies above the visible horizon BF. 
The point C receives a twilight only from the small portion 



Fig. 32. 




of the atmosphere HMG, while at D the twilight has ceased 
altogether. 

The limit of twilight is generally understood to be the in- 
stant when stars of the sixth magnitude begin to be visible 
in the zenith at evening, or disappear in the morning. This 
generally happens when the sun is about 18 degrees below 
the horizon. 

90. Duration of Twilight at the Equator. — The duration 
of twilight depends upon the latitude of the place and the 
sun's declination. At the equator, where the circles of diur- 
nal motion are perpendicular to the horizon, when the sun is 
in the celestial equator it descends through 18 degrees in an 
hour and twelve minutes (xl—l^ hours) ; that is, twilight 
lasts lh. and 12m. When the sun is not in the equator the 
duration of twilight is slightly increased. 

91. Duration of Tioilight at the Poles. — At the north pole, 
since the horizon coincides with the celestial equator, there 
is continued day as long as the sun is north of the equator; 
that is, for a period of six months. Then succeeds a period 
of twilight, which lasts about 50 days, until the sun attains 
a distance of 18 degrees south of the equator. Then suc- 
ceeds a period of about eighty days without twilight, when 
the sun as;ain reaches a south declination of 18 decrees. 
Twilight now commences, and continues for about 50 days, 
and is succeeded by another long day of six months. 

92. Duration of Twilight in Middle Latitudes, — At inter- 



TWILIGHT. 61 

mediate latitudes the duration of twilight may vary from 
lh. 12m. to 50 days. The summer twilights are longer than 
those of winter, and the longest twilight occurs at the sum- 
mer solstice, while the shortest occurs when the sun has a 
small southern declination. In latitude 40°, twilight varies 
from an hour and a half to a little over two hours. 

In latitude 50°, where the north pole is elevated 50 de- 
3 rees above the horizon, the point which is on the meridian 
18 degrees below the north point of the horizon is 68° dis- 
tant from the north pole, and therefore 22 degrees distant 
from the equator. 2s"ow, during the entire month of June, 
the distance of the sun from the equator exceeds 22 degrees ; 
that is, in latitude 50°, there is continued twilight from sun- 
set to sunrise during a period of more than a month. 

In latitude 60°, the period of the year during which twi- 
light lasts through the entire night is about four months. 

93. Consequences if there were no Atmosphere, — If there 
were no atmosphere, none of the sun's rays could reach us 
after his actual setting or before his rising ; that is, the dark- 
ness of midnight would instantly succeed the setting of the 
sun, and it would continue thus until the instant of the sun's 
rising. During the day the illumination would also be much 
less than it is at present, for the sun's light could only pen- 
etrate apartments which were accessible to his direct rays, 
or into which it was reflected from the surface of natural ob- 
jects. On the summits of mountains, where the atmosphere 
is very rare, the sky assumes the color of the deepest blue, 
approaching to blackness, and stars become visible in the 
daytime. 



62 ASTRONOMY 



CHAPTER IV. 

rHE EARTH'S ANNUAL MOTION. — SIDEREAL AND SOLAR TIME. 

EQUATION OF TIME. THE CALENDAR. PARALLAX. — 

PROBLEMS ON THE GLOBES. 

94: Sun*s apparent Motion in Right Ascension. — The sun 

appears to move toward the east among the stars; for if, on 
any evening soon after sunset, we notice the distance of any 
star from the western horizon, we shall find in a few even- 
ings that this distance has grown less, and, since the stars 
themselves all maintain the same position with respect to 
each other, we conclude that the sun has moved toward the 
east. 

If we determine the sun's right ascension from day to day 
witli the transit instrument, we shall find that the right as- 
cension increases each day about one degree, or four minutes 
of time; so that in a year the sun makes a complete circuit 
round the heavens, moving continually among the stars from 
west to east. This daily motion in right ascension is not 
uniform, but varies from 215s. to 2G6s., the average motion 
being about 230s., or 3m. 56s. 

95. iSim's apparent Motion in Declination. — If we observe 
daily with the mural circle the point at which the sun's centre 
crosses the meridian, Ave shall find that its position changes 
continually from day to day. Its declination is zero on the 
20th of March, from which time its north declination in- 
creases until the 21st of June, when it is 23° 27'. It then 
decreases until the 22d of September, when the sun's centre 
is again upon the equator. Its south declination then in- 
creases until the 21st of December, when it is 23° 27^ after 
which it decreases until the sun's centre returns to the equa- 
tor on the 20th of March. 

If we combine these two motions in right ascension and 
declination, and trace upon a celestial globe the course of 



G3 

the sun from day to day through the year, we shall find that 
its path is a great circle of the heavens, whose plane makes 
an angle of 23° 27' with the plane of the celestial equator. 
This circle is called the ecliptic, because solar and lunar 
eclipses can only take place when the moon is very near this 
plane. 

96. The Equinoxes and Solstices. — The ecliptic intersects 
the celestial equator at two points diametrically opposite to 
each other. These are called the equinoctial points, because 
when the sun is at these points it is for an equal time above 
and below the horizon, and the days and nights are there- 
fore equal. 

That one of these points which the sun passes in the spring 
is called the vernal equinoctial point, and the other, which is 
passed in the autumn, is called the autumnal equinoctial 
point. The times at which the sun's centre is found at these 
points are called the vernal and autumnal equinoxes. The 
vernal equinox therefore occurs on the 20th of March, and 
the autumnal on the 22d of September. 

Those points of the ecliptic which are midway between 
the equinoctial points are the most distant from the celestial 
equator, and are called the solstitial points ; and the times 
at which the sun's centre passes these points are called the 
solstices. That which occurs in the summer is called the 
summer solstice, and the other the winter solstice. The sum- 
mer solstice takes place about the 21st of June, and the win- 
ter solstice about the 21st of December. 

The distance of either solstitial point from the celestial 
equator is 23° 27'. The more distant the sun is from the 
celestial equator, the more unequal will be the days and 
nights ; and therefore the longest day of the year will be 
the day of the summer solstice, and the shortest that of the 
winter solstice. In southern latitudes the seasons will be 
reversed. 

97. The Colures. — The equinoctial colure is the hour circle 
which passes through the equinoctial points. The solstitial 
colure is the hour circle which passes through the solstitial 
points. The solstitial colure is at right angles both to the 



64 



ASTRONOMY. 



ecliptic and to the equator, for it passes through the pole of 
each of these circles. 



Fig. 33. 



98. Tropics and Polar Circles. — The tropics are two small 
circles parallel to the equator, and 
passing through the solstices. That 
which is on the north side of the 
equator is called the Tropic of Can- 
cer, and the other the Tropic of 
Capricorn. 

The polar circles are two small 
circles parallel to the equator, and 
distant 23° 2 7' from the poles. The 
one about the north pole is called 
the Arctic circle ; the other, about 
the south pole, is called the Antarctic circle. 

99. The Zodiac. — The zodiac is a zone of the heavens ex- 
tending eight degrees on each side of the ecliptic. The sun, 
the moon, and all the larger planets have their motions with- 
in the limits of the zodiac. 

The ecliptic and zodiac are divided into twelve equal parts 
called signs, each of which contains 30 degrees. Beginning 
at the vernal equinox, and following round from west to east, 
the signs of the zodiac, with the symbols by which they are 
designated, are as follows : 



M - w ' tfcrt] 


bPoV 


y^^Snc 


Cl£CV£>V. 


h-^m±st 


Ca**l£~^\^ 


EQU 


ATOR 






w^^" 


"^^^/ 


\. ^CTIC 


Si ^/ 


^CtLXh, 


r u 



Sign. Symbol. 

I Aries T 

II. Taurus » 

III. Gemini n 

IV. Cancer £p 

V. Leo a 

TIB 



VX Virgo 



Svmbol. 



Sign. 

VII. Libra 

VIII. Scorpio .... 

IX. Sagittarius. 

X. Capricornus 

XL Aquarius £? 

XII. Pisces X 



V3 



The first six are called northern signs, being north of the 
celestial equator; the others are called southern signs. 

The vernal equinox corresponds to the first point of Aries, 
and the autumnal equinox to the first point of Libra. The 
summer solstice corresponds to the first point of Cancer, and 
the winter solstice to the first point of Capricorn. 



THE EARTH'S ANNUAL MOTION. 65 

100. Celestial Latitude and Longitude, — A circle of lati- 
tude is a great circle of the celestial sphere which passes 
through the poles of the ecliptic, and therefore cuts this cir- 
cle at right angles. 

The latitude of a heavenly body is its distance from the 
ecliptic measured on a circle of latitude. It may be north 
or south, and is counted from zero to 90 degrees. 

The longitude of a heavenly body is the distance from the 
vernal equinox to the circle of latitude which passes through 
the centre of the body, and is measured on the ecliptic to- 
ward the east, or in the order of the signs. Longitude is 
counted from zero to 360 degrees. 

The position of a heavenly body is designated by means 
of its longitude and latitude, as w r ell as by its right ascen- 
sion and declination, Art. 31. The former refer to the vernal 
equinox and the ecliptic, the latter to the vernal equinox 
and the equator. 

101. Division of the Earth into Zones. — The earth is nat- 
urally divided into five zones, depending on the appearance 
of the diurnal path of the sun. These zones are, 

1st. The torrid zone, extending from the Tropic of Cancer 
to the Tropic of Capricorn. Throughout this zone the sun 
every year passes through the zenith of the observer, when 
the sun's declination is equal to the latitude of the place. 

2d. The two frigid zones, included within the polar cir- 
cles. Within these zones there are several days of the year, 
Fig. 34. near the winter solstice, during which 

the sun does not rise above the horizon, 
and near the summer solstice there are 
several days during which the sun does 
not sink below the horizon. At the 
summer solstice, on the arctic circle, the 
sun's distance from the north pole is 
just equal to the latitude of the place, 
and the sun's diurnal path just touches 
the horizon at the north point. 

3d. The north and south temperate zones, extending from 
the tropics to the polar circles. Within these zones the sun 
is never seen in the zenith, and it rises and sets every day. 




66 



ASTRONOMY, 



102. Appearances produced by the Earth? s Annual Motion. 
— The apparent annual motion of the sun may be explained 
either by supposing a real revolution of the sun around the 
earth, or a revolution of the earth around the sun. But we 
conclude, from the principles of Mechanics, that the earth 
and sun must both revolve around their common centre of 
gravity, and this point is very near the centre of the sun, 
Art. 147. 

If the earth could be observed by a spectator upon the 
sun, it would appear among the fixed stars in the point of 
the sky opposite to that in which the sun appears as viewed 
from the earth. 

In Fig. 35, let S represent the sun, and ABPD the orbit 

of the earth. To a spec- 
tator upon the earth, the 
sun will appear projected 
among the fixed stars in 
the point of the sky oppo- 
site to that occupied by the 
earth ; and, while the earth 
moves from A to B and P, 
the sun will appear to move 
among the stars from P to 
D and A, and in the course 
of the year will trace out 
in the sky the plane of the 
ecliptic. When the earth is in Libra, we see the sun in the 
opposite sign, Aries ; and while the earth moves from Libra 
to Scorpio, the sun appears to move from Aries to Taurus, 
and so on through the ecliptic. 



Fig. 35. 




V* 1 ' 



103. Cause of the Change of Seasons. — The annual revo- 
lution of the earth around the sun, combined with its diur- 
nal rotation upon its axis, enables us to explain not only the 
alternations of day and night, but also the succession of sea- 
sons. While the earth revolves annually round the sun, it 
has a motion of rotation upon an axis which is inclined 23° 
27' from a perpendicular to the ecliptic; and this axis con- 
tinually points in the same direction. 

In June, when the north pole of the earth inclines toward 



THE EARTHS ANNUAL MOTION. 



67 



the sun, the greater portion of the northern hemisphere is 
enlightened, and the greater portion of the southern hemi- 
sphere is dark. The days are therefore longer than the 
nights in the northern hemisphere, while the reverse is true 
in the southern hemisphere. Upon the equator, however, the 
days and nights are equal. In December, when the south 
pole inclines toward the sun, the days are longer than the 
nights in the southern hemisphere, and the nights are longer 
than the days in the northern hemisphere. 

In March and September, when the earth's axis is perpen- 
dicular to the direction of the sun, the circle which separates 
the enlightened from the unenlightened hemisphere passes 
through the poles, and the days and nights are equal all over 
the globe. 

These different cases are illustrated by Fig. 36. Let S 
represent the position of the sun, and ABCD different posi- 
tions of the earth in its orbit, the axis, ns 9 always pointing 
toward the same fixed star. At A and C (the equinoxes) 
the sun illumines from n to s, and as the globe turns upon its 
axis the sun will appear to describe the equator, and the days 
and nights will be equal in all parts of the globe. When 
the earth is at B (the summer solstice) the sun illumines 23-J 



Fig. 36. 



Summer 




Solstice 



degrees beyond the north pole, n, and falls the same distance 
short of the south pole, s. When the earth is at D (the 
winter solstice) the sun illumines 23^ degrees beyond the 



68 



ASTRONOMY. 



south pole, s, and falls the same distance short of the north 
pole, 71, 

104. In what Case would there have been no Change of 
Seasons. — If the earth's axis had been perpendicular to the 
plane of its orbit, the equator would have coincided with 
the ecliptic, day and night would have been of equal dura- 
tion throughout the year, and there would have been no di- 
versity of seasons. 

105. In what Case would the Change of Seasons have been 
greater than it now is? — If the inclination of the equator to 
the ecliptic had been greater than it is, the sun would have 
receded farther from the equator on the north side in sum- 
mer, and on the south side in winter, and the heat of sum- 
mer, as well as the cold of winter, would have been more in- 
tense ; that is, the diversity of the seasons would have been 
greater than it is at present. If the equator were at right 
angles to the ecliptic, the poles of the equator would be sit- 
uated in the ecliptic; and at the summer solstice the sun 
would appear at the north pole of the celestial sphere, while 
at the winter solstice it would be at the south pole of the 
celestial sphere. To an observer in the middle latitudes the 
sun would therefore, for a considerable part of summer, be 
within the circle of perpetual apparition, and for several 
weeks be constantly above the horizon. So also for a con- 
siderable part of winter he would be within the circle of 
perpetual occultation, and for several weeks be constantly 
below the horizon. The great vicissitudes of heat and cold 
resulting from such a movement of the sun would be ex- 
tremely unfavorable to both animal and vegetable life. 

106. To Determine the Obliquity of the Ecliptic. — The ob- 
liquity of the ecliptic, that is, the inclination of the equator 
to the ecliptic, is equal to the greatest declination of the 
sun. It may therefore be determined by measuring with a 
mural circle the sun's declination at the summer or at the 
winter solstice. The mean value of the obliquity in Jan., 
1868, was 23° 27' 23". The obliquity is diminishing at the 
rate of about half a second annually. 



FORM OF THE EARTH'S ORBIT. 



69 




107. To determine the Form of the Earth? s Orbit. — The 
form of the earth's orbit could be determined if we knew 
the direction of the sun from the earth for each day of the 
year, and also his daily distances from the earth either abso- 
lute or relative. Now the direction of the sun is indicated 
by his longitude, which can be determined by observation. 

To determine the sun's absolute distance from us requires 
a knowledge of his parallax, which will be exj^lained hereaft- 
er, Art. 145 ; but his relative distances from day to day are 
indicated by his apparent diameters, since the apparent di- 
ameter of the sun at different distances from the earth varies 
inversely as the distance. Thus, if AB represents the sun 
Fig. 37. seen from the earth at E, 

it is evident that, the 
greater the distance, the 
less will be the angle AE 
B. By measuring with a 
micrometer the sun's apparent diameter from day to day 
throughout the year, we have a measure of the relative dis- 
tances ; and if we also observe the sun's longitude for every 
day of the year, by combining the two series of observations 
we may determine the form of the earth's orbit. If the sun's 
longitude be increased by 180 degrees, it will represent the 
direction of the earth as seen from the sun, Art. 102. We 
then construct a figure by drawing lines SA, SB, etc., to 
Fig38. represent the direction of the 

earth from the sun for each 
day of the year, and set off 
the distances SA, SB, etc., 
equal to the relative distances 
already determined by the ob- 
servations. Then, connecting 
the points A, B, C, D, etc., by 
a curve line, we have a figure 
which represents the earth's 
*^~ """■k orbit. This orbit is found to 

differ but little from a circle, but more accurately it is an 
ellipse, with the sun occupying one of the foci. 




108. To find the Eccentricity of the Earth's Orbit— The 



70 



ASTRONOMY. 



eccentricity of an ellipse measures its deviation from the 
form of a circle. It is the distance between the two foci di- 
vided by the major axis. Its value can be deduced from 
the greatest and least apparent diameters of the sun, since 
these furnish a measure of the relative distances. The great- 
est and least apparent diameters are 32'.61 and 31 '.53. The 
distances SG and SA are in the ratio of the same numbers. 
Their sum is 64'. 14, and their difference l'.08. Hence the 
eccentricity of the ellipse is -g^TT? or -ro very nearly. This 
quantity is so small that if a diagram were drawn repre- 
senting the earth's orbit with perfect accuracy, we could 
not, without careful measurement, discern any deviation from 
an exact circle. 

The point A of the orbit where the earth is nearest the 
sun is called the perihelion, and the earth passes this point 
on the 1st of January. The point G, most distant from the 
sun, is called the aphelion, and the earth passes this point on 
the 1st of July; that is, the earth is more distant from the 
sun in summer than in winter by one thirtieth of the mean 
distance. 



109. Why the greatest Heat and Cold do not occur at the 
Solstices. — The influence of the sun in heating the earth's 
surface depends upon its altitude at noon, and upon the 
length of time during which it continues above the horizon. 
Both these causes conspire to produce the increased heat of 
summer and the diminished heat of winter. If the temper- 
ature at any place depended simply upon the direct mo- 
mentary influence of the sun, the hottest day would occur 
at the summer solstice when the sun rises highest and the 
days are the longest ; but during the most of summer the 
heat received from the sun during the day is greater than 
the loss by radiation during the night, and the maximum 
occurs when the loss by night is just equal to the gain by 
day. At most places in the northern hemisphere this oc- 
curs some time in July or August. 

For the same reason, the greatest cold does not occur at 
the winter solstice, but some time in January or February, 
when the gain of heat by day is just equal to the loss bv 
night. 



RADIUS VECTOR OF THE EARTH'S ORBIT. 



71 



The variation in the distance of the sun from the earth 
exerts no appreciable influence upon the difference of sea- 
sons, because, when this distance is least, the angular veloc- 
ity of the earth about the sun is greatest ; and hence, in that 
half of the orbit which is most remote from the sun, we re- 
ceive the same amount of heat as in the half of the orbit 
which is nearest the sun. 



Fte. 39. 




110. The Radius Vector of the Earth? s Orbit describes 
equal Areas in equal Times. — The straight line drawn from 
the centre of the sun to the centre of the earth is called the 
radius vector of the earth's orbit. If we suppose S to rep- 
resent the place of the sun, and 
A and B to represent the places 
of the earth at noon on two suc- 
cessive days, then the figure ASB 
will be the area described by the 
radius vector of the earth in one 
day. Knowing the relative dis- 
tances of AS, BS, and also the an- 
gle ASB, as explained in Art. 107, 
we can compute the area of the 
triangular space ASB. If, in like 

manner, we suppose lines to be drawn from the sun to the 
places occupied by the earth at noon for each day of the 
year, the triangular spaces thus formed will all be found to 
be equal to each other. Hence it is established by observa- 
tion that the radius vector of the earth's orbit describes 
equal areas in equal times. 

111. To find the Latitude of any Place. — The latitude of 
a place may be determined by measuring the altitude of 
any circumpolar star, both at its upper and lower culmina- 
tions, as explained in Art. 72. It 
may also be determined by measur- 
ing a single meridian altitude of 
any celestial body whose declina- 
tion is known. Let HO represent 
the horizon of a place, Z the zenith, 
P the elevated pole, and EQ the 



Fig. 40. 




72 ASTRONOMY. 

equator. Let S or S' be a star upon the meridian ; then SE 
or S'E will represent its declination. Measure SH, the alti- 
tude of the star, and correct the altitude for the effect of re- 
fraction. Then 

EH=SH-8E=S'H-{-8'E. 
Hence EH, which is the altitude of the equator, becomes 
known ; and hence PO, the latitude of the place, is known, 
since PO is the complement of EH. The declinations of all 
the brighter stars have been determined with great accu- 
racy, and are recorded in catalogues of the stars. 

112. To find the Latitude at Sea. — At sea the latitude is 
usually determined by measuring with a sextant the great- 
est altitude of the sun's lower limb above the sea horizon at 
noon. The observations should be commenced about half 
an hour before noon, and the altitude of the sun be repeat- 
edly measured until the altitude ceases to increase. This 
greatest altitude is considered to be the sun's altitude when 
on the meridian. To this altitude we must add the sun's 
semidiameter in order to obtain the altitude of the sun's 
centre, and this result must be corrected for refraction. To 
this result we must add the declination of the sun when it 
is south of the equator, or subtract it when north, and we 
shall obtain the elevation of the equator, which is the com- 
plement of the latitude. The sun's declination for every 
day in the year is given annually in the Nautical Almanac. 

113. Sidereal Time. — Sidereal time is time reckoned in 
sidereal days, hours, etc. A sidereal day is the interval be- 
tween two successive returns of the vernal equinox to the 
same meridian. This interval represents the time of the 
earth's rotation upon its axis, and is not only invariable 
from one month to another, but has not changed so much 
as the hundredth part of a second in two thousand years. 

114. Solar Time. — Solar time is time reckoned in solar 
days, hours, etc. A solar day is the interval between two 
successive returns of the sun to the same meridian. 

The sun moves through 360 degrees of longitude in one 
tropical year, or 365 days, 5 hours, 48 minutes, and 47 sec* 






SIDEREAL AND SOLAR TIME COMPARED. 73 

onds. Hence the sun's mean daily motion in longitude is 
found by the proportion 

One year : one day :: 360° : 59' 8"=the daily motion. 
This motion is not uniform, but is most rapid when the 
sun is nearest to the earth. Hence the solar days are un- 
equal ; and to avoid the inconvenience which would result 
from this fact, astronomers employ a mean solar day, whose 
length is equal to the mean or average of all the apparent 
solar days in a year. 

115. Sidereal and Solar Time compared. — The length of 
the mean solar day is greater than that of the sidereal, be- 
cause when, in its diurnal motion, the mean sun returns to 
a given meridian, it is 59' 8" eastward (with respect to the 
fixed stars) of its position on the preceding day. 

Hence, in a mean solar day, an arc of the equator equal to 
360° 59' 8" passes over the meridian, while only 360° pass in 
a sidereal day. The excess of the solar day above the side- 
real day will then be given by the proportion 
360° : 59'' 8" : : one day : 3m. 56s. 

Hence 24 hours of mean solar time are equivalent to 24h. 
3m. 56s. of sidereal time; and 24 hours of sidereal time are 
equivalent to 23h. 56m. 4s. of mean solar time, omitting, for 
convenience, the fractions of a second. 

116. Civil Day and Astronomical Day. — The civil day 
begins at midnight, and consists of two periods of 12 hours 
each ; but modern astronomers number the hours continu- 
ously up to 24, and commence the day at noon, because this 
date is marked by a phenomenon which can be easily ob- 
served, viz. the passage of the sun over the meridian ; and 
because, since observations are chiefly made at night, it is 
inconvenient to have a change of date at midnight. The 
astronomical day commences 12 hours later than the civil 
day. Thus, July 4th, 9 A.M., civil time, corresponds to July 
3d, 21 hours of astronomical time. 

117. Ap>parent Time and Mean Time. — An apparent solar 
day is the interval between two successive transits of the 
sun's centre over the same meridian. Apparent time is time 

D 



74 ASTRONOMY. 

reckoned in apparent solar days, while mean time is time 
reckoned in mean solar days. The difference between ap- 
parent solar time and mean solar time is called the equation 
of time. 

If a clock were required to indicate apparent solar time, 
it would be necessary that its rate should change from day 
to day, according to a very complicated law. It has been 
found in practice so difficult to accomplish this, that clocks 
are now generally regulated to indicate mean solar time. 
Such a clock will not, therefore, generally indicate exactly 
12 hours when the sun is on the meridian, but will some^ 
times indicate a few minutes more than 12 hours, and some- 
times a few minutes less than 12 hours ; the difference being 
equal to the equation of time. 

118. First Cause of the Inequality of the Solar Days. — 
The inequality of the solar days depends on two causes, the 
unequal motion of the earth in its orbit, and the inclination 
of the equator to the ecliptic. 

While the earth is revolving round the sun in an elliptic 
orbit, its motion is most rapid when it is nearest to the sun, 
and slowest when it is most distant. Let ADGK represent 

the elliptic orbit of the earth, 
with the sun in one of its foci 
at S, and let the direction of 
motion be from A toward B. 
We have found that the 
sun's mean daily motion as 
seen from the earth y or the 
earth's mean daily motion as 
seen from the sun, is 59' 8." 
But when the earth is nearest 
the sun at A, its daily motion 
is 61 10", while at G, when most remote from the sun, it is 
only 51' 12". While moving, therefore, from A to G, the 
earth will be in advance of its mean place ; but at G, having 
completed a half revolution, the true and the mean places 
will coincide. For a like reason, in going from G to A, the 
earth will be behind its mean place ; but at A the true and 
the mean places will again coincide. The point A in the di- 
agram corresponds to about the 1st of January. 




INEQUALITY OF SOLAR DAYS. 



75 



So far, then, as it depends upon the unequal motion of the 
earth in its orbit, the difference between apparent time and 
mean time will be zero on the 1st of January ; but after this, 
mean time will be in advance of apparent time, and the dif- 
ference will go on increasing for about three months, when 
it amounts to a little more than 8 minutes. From this time 
the difference will diminish until about the 1st of July, when 
it becomes zero ; after this, apparent time will be in advance 
of mean time, and the difference will go on increasing for 
about three months, when it amounts to a little more than 8 
minutes, from which time the difference will diminish until 
the 1st of January, when apparent time and mean time 
a^ain coincide. 



119. Second Cause for the Inequality of the Solar Days.-^ 
Even if the earth's motion in its orbit were perfectly uni- 
form, the apparent solar days would be unequal, because the 
ecliptic is inclined to the equator. Let A^N represent half 



Fig. 42. 




* f g & 



71U K 



the equator, and AGN the northern half of the ecliptic. 
Let the ecliptic be divided into equal portions, AB, BC, etc., 
supposed to be described by the sun in equal portions of 
time; and through the points B, C, D, etc., let hour circles 
be drawn cutting the equator in the points 5, c, d, etc. Then 
AB, BC, etc., represent arcs of longitude, while A J, 5c, etc., 
represent the corresponding arcs of right ascension. The 
arc AGN is equal to the arc A</N, for all great circles bi- 
sect each other ; and therefore AG, the half of AGN", is equal 
to Ag, the half of A#N. Now , since AB£ is a right-angled 
triangle, AB is greater than Ab / for the same reason, AC is 



76 ASTRONOMY. 

greater than Ac, etc. But FG is less than/^r ; that is, Kg is 
divided into unequal portions at the points &, c, d, etc. 

Thus we see that if the daily motion in longitude were 
uniform, the daily motion in right ascension would not be 
uniform, but would be least near the equinoxes, where the 
arc of longitude is most inclined to the arc of right ascen- 
sion, and greatest near the solstices, where the two arcs be- 
come parallel to each other. 

Suppose, then, that a fictitious sun (which we will call the 
mean sun) moves uniformly along the equator, while the real 
sun moves uniformly along the ecliptic, and let them start 
together at the vernal equinox. From the vernal equinox 
to the summer solstice the right ascension of the mean sun 
will be greater than that of the real sun, but at the summer 
solstice the difference will vanish. In the second quadrant 
the right ascension of the mean sun will be less than that of 
the true sun, but at the autumnal equinox they will again 
coincide. In the third quadrant the right ascension of the 
mean sun will be greater than that of the true sun, while in 
the fourth quadrant it will be less. 

The amount of the equation of time depending upon the 
obliquity of the ecliptic varies from zero to nearly 10 min- 
utes. It is negative for three months, then positive for 
three months; then negative for three months, and then 
positive for another three months. 

The actual value of the equation of time will be found by 
taking the algebraic sum of the effects due to these two sep- 
arate causes. The result is that there are four periods of the 
year when the equation is zero, and the equation, when great- 
est, amounts to 1 6 minutes. The equation of time for each 
day of the year is given in the Nautical Almanac, and it is 
also stated approximately upon most celestial globes. 

120. To find the Time at any Place. — The time of appa- 
rent noon is the time of the sun's meridian passage, and is 
most conveniently found by means of a transit instrument 
adjusted to the meridian. Mean time may be derived from 
apparent time by applying the equation of time with its 
proper sign. 

The time of apparent noon may also be found by noting 



TO TRACE A MERIDIAN LINE. 



71 



the times when the sun has equal altitudes before and after 
noon, and bisecting the interval between them. When great 
accuracy is required, the result obtained by this method re- 
quires a slight correction, since the sun's declination changes 
in the interval between the observations. 



121. To trace a Meridian Line. — At the instant of noon, 
the shadow cast by a vertical rod upon a horizontal plane is 
the shortest, and the line marked at that instant by the shad- 
ow is a meridian line. Since, however, near the time of noon, 
the length of the shadow changes very slowly, this method 
is not susceptible of much precision. The following method 
is more accurate : 



Fig. 43. 




Upon a horizontal plane draw a series of concentric cir- 
cles, and at the centre of the circles erect a vertical rod of 
wood or brass. During the forenoon, observe the instant 
when the vertex of the shadow of the rod falls upon the out- 
er circle, and mark the point A. Mark also the point B, 
where the vertex of the shadow crosses the second circle, 
the point C, w x here it crosses the third circle, etc. In the 
afternoon, mark in like manner the points C, B', A', where 
the vertex of the shadow crosses the same circles. Bisect 
the arcs AA', BB', CC, etc. ; the line NS, passing through 
the points of bisection, will be a meridian line. 

Having established a meridian line, the time of apparent 
noon will be indicated by the passage of the shadow of the 
rod over this line. 



78 



ASTRONOMY. 



Fig. 44. 



122* A Sun-dial. — If we draw a line, AB, parallel to the 
axis of the earth, the plane passing through the sun and this 
line will advance uniformly 15 degrees each hour. If the 
line here supposed be a slender metallic rod, its shadow will 
advance each hour 15 degrees about a circle perpendicular 
to the axis of the earth ; and this shadow, cast upon a hori- 
zontal plane, will have the same direction at any given hour 
at all seasons of the year. If, then, we graduate this hori- 
zontal plane in a suitable 
manner, and mark the 
lines with the hours of 
the day, we may deter- 
mine the apparent time 
whenever the sun shines 
upon the rod. Such an 
instrument is called a 
sun-dial^ and for many 
centuries this was the 
principal means relied 
upon for the determina- 
tion of time. This in- 
strument will always in- 
dicate apparent time ; but mean time may be deduced from 
it by applying the equation of time. 

123. To find the Time by a single Altitude of the Sim. — 
The time may also be computed from an altitude of the sun 
measured at any hour of the day, provided we know the lati- 
tude of the place and the sun's declination. 

Fig. 45. z I jet PZH represent the meridian 

of the place of observation, P the 
pole, Z the zenith, and S the place 
of the sun. Measure the sun's ze- 
nith distance ZS, and correct it for 
H ° refraction. Then in the spherical 

triangle ZPS we know the three sides, viz., PZ, the comple- 
ment of the latitude ; PS, the distance of the sun from the 
north pole ; and ZS, the sun's zenith distance. In this trian- 
gle we can compute by trigonometry the angle ZPS, which, 
if expressed in time, will be the interval between noon and 





JULIAN AND GREGORIAN CALENDARS. s 79 

the moment of observation. This observation can be made 
at sea with a sextant, and this is the method of determining 
time which is commonly practiced by navigators. 

124. The Julian Calendar. — The interval between two 
successive returns of the sun to the vernal equinox is called 
a tropical year. Its average length, expressed in mean solar 
time, is 365d. 5h. 48m. 48s. But in reckoning time for the 
common purposes of life, it is convenient to make the year 
consist of a certain number of entire days. In the calendar 
established by Julius Caesar, and hence called the Julian 
Calendar, three successive years were made to consist of 
365 days each, and the fourth of 366 days. The year which 
contained 366 days was called a bissextile year, because the 
6th of the kalends of March was twice counted. Such a 
year is now commonly called leap year, and the others are 
called common years. The odd day inserted in a bissextile 
year is called the intercalary day. 

The reckoning by the Julian calendar supposes the length 
of the year to be 365^ days. A Julian year therefore ex- 
ceeds the tropical year by 11m. 12s. This difference amounts 
to a little more than three days in the course of 400 years. 

125. The Gregorian Calendar. — At the time of the Coun- 
cil of Nice, in the year 325, the Julian calendar was adopt- 
ed by the Church, and at that time the vernal equinox fell 
on the 21st of March; but in the year 1582 the error of the 
Julian calendar had accumulated to nearly 10 days, and the 
vernal equinox fell on the 11th of March. If this erroneous 
reckoning had continued for several thousand years, spring 
would have commenced in September, and summer in De- 
cember. It was therefore resolved to reform the calendar, 
which was done by Pope Gregory XIII., and the first step 
was to correct the loss of the ten days by counting the day 
succeeding the 4th of October, 1582, the 15th of the month 
instead of the 5th. In order to prevent the recurrence of 
the like error in future, it was decided that three intercalary 
days should be omitted every four hundred years. It was 
also decided that the omission of the intercalary days should 
take place in those years which are divisible by 100, but not 



80 



ASTRONOMY. 



by 400. Thus the years 1700, 1800, and 1900, which in the 
Julian calendar are bissextile, in the Gregorian calendar are 
common years of 365 days. The error of the Gregorian cal- 
endar amounts to less than one day in 3000 years. 

126. Adoption of the Gregorian Calendar. — The Grego- 
rian Calendar was immediately adopted at Rome, and soon 
afterward in all Catholic countries. In Protestant countries 
the reform was not so readily adopted, and in England and 
her colonies it was not introduced till the year 1752. At 
this time there was a difference of 1 1 days between the Ju- 
lian and Gregorian calendars, in consequence of the suppres- 
sion in the latter of the intercalary day in 1700. It was 
therefore decided that 1 1 days should be struck out of the 
month of September, 1752, by calling the day succeeding the 
2d of the month the 14th instead of the 3d. 

The Julian and Gregorian calendars are frequently desig- 
nated by the terms old style and new style. In consequence 
of the suppression of the intercalary day in the year 1800, 
the difference between the two calendars now amounts to 12 
days. Russia, and the Greek Church generally, still adhere 
to the old style, consequently their dates are thus express- 



ed: 1868 



June 22. 
July 4. 



127. Diurnal Parallax explained. — The direction in 
which a celestial body would be seen if viewed from the 
centre of the earth is called its true place, and the direction 
in which it is seen from any point on the surface is called 

its apparent place. The arc 
of the heavens intercepted 
between the true and appar- 
ent places, that is, the ap- 
parent displacement which 
would be produced by the 
transfer of the observer from 
the centre to the surface of 
the earth, is called the diur- 
nal parallax. 

Let C denote the centre of 
the earth, P the place of an 




PARALLAX. 81 

observer on its surface, M an object (as the moon) seen in 
the zenith at P, M' the same object seen at the zenith dis- 
tance MPM', and M" the same object seen in the horizon. 

It is evident that M will appear in the same direction, 
whether it be viewed from P or C. Hence in the zenith 
there is no diurnal parallax, and there the apparent place 
of an object is its true place. 

If the object be at M', its apparent direction is PM' while 
its true direction is CM', and the parallax corresponding to 
the zenith distance MPM' will be PM C. 

As the distance of the object from the zenith increases, 
the parallax increases ; and when the object is in the hori- 
zon as at M", the diurnal parallax becomes greatest, and is 
called the horizontal parallax. It is the angle which the 
earth's radius subtends to an observer supposed to be sta- 
tioned upon the object. 

It is evident that parallax increases the zenith distance, 
and consequently diminishes the apparent altitude. Hence, 
to obtain the true zenith distance from the apparent, the 
parallax must be subtracted ; and to obtain the apparent ze- 
nith distance from the true, the parallax must be added. 
The azimuth of a heavenly body is not affected by parallax. 

128. To determine the Parallax of a Heavenly Body by 
F is- 47. Observation. — Let A, A' be 

two places on the earth situ- 
ated under the same meridi- 
an, and at a great distance 
from each other, one in the 
northern hemisphere, and the 
other in the southern ; let C 
be the centre of the earth, and 
M the body to be observed 
(the moon, for example). Let an observer at each of the 
stations measure the zenith distance of the moon when on 
the meridian, and correct the measured distance for the ef- 
fect of refraction. This will furnish the angles ZAM and 
Z'A'M. But the angle ZCZ' is the sum of the latitudes of 
the two stations, which are supposed to be known. Hence 
we can obtain the angle AMA', which is the sum of the par- 

D2 




82 ASTRONOMY. 

allaxes at the two stations, and from this we can compute 
what would be the parallax if the object were seen in the 
horizon ; that is, we can deduce the horizontal parallax. 

It is not essential that the two observers should be exact- 
ly on the same meridian ; for if the meridian zenith distances 
of the body be observed from day to day, its daily variation 
will become known. Then, knowing the difference of longi- 
tude of the two places, we may reduce the zenith distance 
observed at one of the stations to what it would have been 
if the observations had been made in the same latitude on 
the meridian of the other station. 

129. Results obtained by this Method. — By combining ob- 
servations made at the Cape of Good Hope with those made 
at European observatories, the moon's parallax has been de- 
termined with great precision. This parallax varies consid- 
erably from one day to another. The horizontal parallax, 
when greatest, is about 61', and when least 53', the average 
value being about 57', or a little less than one degree. 

The parallax of the sun and planets can be determined in 
the same manner; but these parallaxes are very small, and 
there are other methods by which they can be more accu- 
rately determined. 

When we know the earth's radius and the horizontal par- 
allax of a heavenly body, we can compute its distance. For 
(Fig. 46), 

sin. PM"C : PC : : radius : CM", 
or the distance of a heavenly body from the centre of the 
earth is equal to the radius of the earth divided by the sine 
of the horizontal parallax. 

ADDITIONAL PROBLEMS ON THE TERRESTRIAL GLOBE. 

130. To find the Surfs Longitude for any given Day. — 
Find the given month and day on the wooden horizon, and 
the sign and degree corresponding to it in the circle of signs 
will show the sun's place in the ecliptic ; find this place on 
the ecliptic, and the number of degrees between it and the 
first point of Aries, counting from the first of Aries toward 
the east, will be the sun's longitude. 

Ex. 1. What is the sun's longitude Feb. 22d ? Ans. 333°. 



PROBLEMS ON THE TERRESTRIAL GLOBE. 83 

Ex. 2. What is the sun's longitude July 4th ? Arts. 102°. 
Ex. 3. What is the sun's longitude Oct. 25th ? Ans. 212°. 

13L To find the Surfs right Ascension and Declination 
for any given Day. — Bring the sun's place in the ecliptic to 
the graduated edge of the brass meridian ; then the degree 
of the equator under the brass meridian will be the right 
ascension, and the degree of the meridian directly over the 
place will be the declination. 

Ex. 1. What is the sun's right ascension July 4th? 

Ans. 104°, or 6h. 56m. 
Ex. 2. What is the sun's right ascension Feb. 22d? 

Ans. 335°, or 22h. 20m. 
Ex. 3. What is the sun's declination July 4th ? 

Ans. 23° 1ST. 
Ex. 4. What is the sun's declination Feb. 22d? 

Ans. 10 °S. 
The right ascension, declination, longitude and latitude 
of the sun, moon, and principal planets, are given in the 
Nautical Almanac for each day of the year. 

132. To find the Sun's Meridian Altitude for any Day of 
the Year. — Make the elevation of the pole above the wooden 
horizon equal to the latitude of the place, so that the wood- 
en horizon may represent the horizon of that place. Bring 
the sun's place in the ecliptic to the brass meridian, and the 
number of degrees on the meridian from the sun's place to 
the horizon will be the meridian altitude. 

Ex. 1. Find the sun's meridian altitude at New York Feb. 
22d. Ans. 39°. 

Ex. 2. Find the sun's meridian altitude at London July 
4th. Ans. 61|°. 

Ex. 3. Find the sun's meridian altitude at Ceylon Oct. 
25th. Ans. 70°. 

133. To find the Surfs Amplitude at any Place and for 
any Day of the Year. — Elevate the pole to the latitude of 
the place, then bring the sun's place in the ecliptic to the 
eastern or western edge of the horizon, and the number of 
degrees on the horizon from the east or west point will be 
the amplitude. 



84 ASTRONOMY. 

Ex. 1. Find the sun's amplitude at New York July 4th. 

Ans. 31° N. 
Ex. 2. Find the sun's amplitude at London Feb. 22d 

Ans. 16° S. 
Ex. 3. Find the sun's amplitude at Ceylon Oct. 25th. 

Ans. 13° S. 

134. To find the Sun's Altitude and Azimuth at any Place 
for any Day and Hour. — Elevate the pole to the latitude 
of the place ; then bring the sun's place in the ecliptic to the 
brass meridian, and set the hour index to XII. Then turn 
the globe eastward or westward, according as the time is 
before or after noon, until the index points to the given 
hour. Screw the quadrant of altitude over the zenith of the 
globe, and bring its graduated edge over the sun's place in 
the ecliptic ; the number of degrees on the quadrant from 
the sun's place to the horizon will be the altitude, and the 
number of degrees on the horizon from the meridian to the 
edge of the quadrant will be the azimuth. 

Ex. 1. Find the altitude and azimuth of the sun at New 
York, Feb. 22d, at 9 A.M. 

Ans. Altitude 26° ; Azimuth S. 49° E. 
Ex. 2. At London, July 4th, at 7 A.M. 

Ayis. Altitude 28° ; Azimuth N. 86° E. 
Ex. 3. At Ceylon, October 25th, at 3| P.M. 

Ans. Altitude 33°; Azimuth S. 72° W. 

135. To find at what Places the Sun is Vertical at Noon 
on any Pay of the Year. — When the sun's declination is 
equal to the latitude of the place, the sun at noon will ap- 
pear in the zenith. Therefore, find the sun's declination, 
and note the degree upon the brass meridian ; revolve the 
globe, and all places which pass under that point will have 
the sun vertical at noon. 

If we wish to know on what two days of the year the sun 
is vertical at any place in the torrid zone, revolve the globe, 
and observe what two points of the ecliptic pass under that 
degree of the brass meridian which corresponds to the lati- 
tude of the place ; the days which correspond to these points 
on the circle of signs will be the days required. 






PROBLEMS ON THE TERRESTRIAL GLOBE. 85 

Ex. 1. At what places is the sun vertical April 15th? 

Ans. All places in lat. 10° N". 
Ex. 2. At what places is the sun vertical Nov. 21st? 

Ans. All places in lat. 20° S. 
Ex. 3. On what two days of the year is the sun vertical at 
Madras ? Ans. April 24 and Aug. 18. 

136, To find the Time of the Sim's Rising and Setting at 
a given Place on a given Day, and also the Length of the 
Day and of the Night. — Elevate the pole to the latitude of 
the place; find the sun's place in the ecliptic; bring it to the 
meridian, and set the hour index to XII. Turn the globe 
till the sun's place is brought down to the eastern horizon ; 
the hour index will show the time of the sun's rising Turn 
the globe till the sun's place comes to the western horizon ; 
the hour index will show the time of the sun's setting. 

Double the time of its setting will be the length of the 
day, and double the time of rising w T ill be the length of the 
night. 

Ex. 1. At what time does the sun rise and set at Wash- 
ington Aug. 18th? Ans, Sun rises at 5^h., and sets at 6|h. 

Ex. 2. At what time does the sun rise and set at Berlin 
July 4th? Ans. Sun rises at 3|h.,and sets at 8^h. 

At any place in the northern hemisphere not within the 
polar circle, the longest day will be at the time of the sum- 
mer solstice, and the shortest day at the time of the winter 
solstice. 

Ex. 3. What is the length of the longest day at Berlin, 
and w T hat is the length of the shortest day ? 

Ans. Longest day 16h. 50m. ; shortest day Yh. 10m. 

The following table shows the length of the longest days 
in different latitudes from the equator to the poles : 

Latitude. Longest Day. 

0° 0' (Equator) 12 hours. 

30° 48' 14 " 

49° 2' 16 " 

58° 27' 18 " 

63° 23' 20 " 

137. To find the Beginning, End, and Duration of con* 



Latitude. 


Longest Day. 


65° 48 / 


. 22 hours. 


66° 32' 


. 24 " 


69° 51' 


. 2 months. 


78° 11" 


. 4 " 


90° 0' (Pole) . 


. 6 



86 ASTRONOMY. 

stant Day at any Place within the Polar Circles. — At any- 
place in the northern hemisphere, the sun at midnight will 
just graze the northern horizon when the sun's north declina- 
tion is equal to the distance of the place from the north pole. 
Therefore note on the brass meridian that degree of north 
declination which is equal to the polar distance of the place; 
revolve the globe, and the two points of! lie ecliptic which 
pass under that degree will be the sun's places at the begin- 
ning and end of constant day. The month and day corre- 
sponding to each of these places will be the times required. 
The interval between these dates will be the duration of 
constant day. 

Ex. Find the beginning and end of constant day in hit. 
75° N. Ans. Begins April 30th and ends Aug. 11th. 

138. To find the Time of the Beginning and End of Twi- 
light. — Elevate the pole to the latitude of the place; find the 
sun's place and bring it to the meridian, and set the hour 
index at XII. Screw the quadrant of altitude over the 
zenith of the globe, and bring the sines place below the 
eastern horizon until, it coincides with the 18th degree on 
the quadrant. The hour index will then mark the beginning 
of twilight. The end of twilight may be found in the same 
manner by bringing the sun's place below the western hori- 
zon. The difference between the time of sunrise and the be- 
ginning of morning twilight will be the duration of twilight. 

fife. 1. What is the beginning and duration of morning 
twilight at Boston July 1st? 

Ans. Begins 2h. 12m. ; duration 2h. 15m. 

Efe. 2, What is the end and duration of evening twilight 
at Berlin Aug. 1st? Ans. Ends at lOh. 45m.; duration 3h. 

PROBLEMS ON THE CELESTIAL GLOBE. 

139. To find the right Ascension and Declination of a 
Star. — Bring the star to the brass meridian; 1 ho degree of 
the meridian directly over the star will be its declination, 
and the degree on the equinoctial under the brass meridian 
will be its right ascension. Right ascension is sometimes 
expressed in hours and minutes of time, and sometimes in 
degrees and minutes of arc. 



PROBLEMS ON THE CELESTIAL GLOBE. 87 

Verify the following by the globe: 





R. A. 


Dec. 


1 


R. A. 


Dec. 


AMebaran.. 


. 4h. 28m. 


16° 14' N. 


Regulus.... 


.. lOh. lm. 


12° 3G' N. 


Birius 


. Gh. 39m. 


16° 32' S. 


1 Arcturus... 


.. 14h. 9m. 


19° 52' N. 



140. The Right Ascension and Declination of a Star being 
given, to find the Star upon the Globe. — Bring the degree of 
the equator which marks the right ascension to the brass 
meridian ; then under the given declination marked on the 
meridian will be the star required. 

Ex 1. What star is in R. A. 5h. 6m. , and Dec. 45° 51' N. ? 

Ans. Capella. 
Ex 2. What star is in R. A. 18h. 32m., and Dec. 38°39 / X? 

Ans. Vega. 
Ex 3. What star is in R. A. 16h. 21m., and Dec. 26° 8' S. ? 

Ans. Antares. 

141 To find the Distance betioeen two Stars. — Place the 
quadrant of altitude so that its graduated edge may pass 
through both stars, and the point marked may be on one 
of them. Then the point of the quadrant which is over the 
other star will show the distance between the two stars. 
Ex. 1. Find the distance of Aldebaran from Sirius. 

An s. 46 degrees. 
Ex. 2. Find the distance of Sirius from Regulus. 

Ans. 58 degrees. 
Ex. 3. Find the distance of Arcturus from Vega. 

Ans. 59 degrees. 

142. To find the Appearance of the Heavens at any Place 
at a given Day and Hour. — Set the globe so that the brass 
meridian shall coincide with the meridian of the place ; ele- 
vate the pole to the latitude of the place ; bring the sun's 
place in the ecliptic to the meridian, and set the hour index 
at XIL ; then turn the globe westward until the index points 
to the given hour. The constellations will then have the 
same appearance to an eye situated at the centre of the 
globe as they have at that moment in the heavens. The 
altitude and azimuth of any star at that instant can thus be 
measured on the globe. 



88 ASTRONOMY. 

Ex. 1. Required the appearance of the heavens at New 
Haven, lat. 41° 18', July 4th, at 10 o'clock P.M. 

Ex. 2. What star is rising near the east at 8 P.M. on the 
20th of October at New York ? Ans. Aldebaran. 

143. To determine the Time of Rising, Setting, and Cul- 
mination of a Star for a given Day and Place. — Elevate 
the pole to the latitude of the place ; bring the sun's place 
in the ecliptic to the meridian, and set the hour index at 
XII. Turn the globe until the star conies to the eastern 
horizon, and the hour shown by the index w T ill be the time 
of the star's rising. Bring the star to the brass meridian, 
and the index w r ill show the time of the star's culmination. 
Turn the globe until the star comes to the western horizon, 
and the index will show the time of the star's setting. 

Ex. Required the time when Aldebaran rises, culminates, 
and sets at Cincinnati, October 10th. 

144i To determine the Position of the Moon or a Planet 
in the Heavens at any given Time and Place. — Find the 
right ascension and declination of the body for the given 
day from the Nautical Almanac, and mark its place upon 
the globe ; then adjust the globe as in Art. 142, and the po- 
sition of the body upon the globe will correspond to its po- 
sition in the heavens. We may then determine the time of 
its rising and setting, as in Art. 143. The time of rising 
and setting of a comet may be determined in the same 
manner. 



THE SUN — ITS PHYSICAL CONSTITUTION. 89 



CHAPTER V. 

THE RUN — ITS PHYSICAL CONSTITUTION. 

145. Distance of the Sun. — The distance of the sun from 
the earth can be computed when we know its horizontal 
parallax and the radius of the earth, Art. 129. There is 
some uncertainty respecting the exact value of the sun's 
parallax, but its mean value is very near 8". 9; and the 
equatorial radius of the earth is 3963 miles. 

I Ience, sin. 8". 9 : 1 : : 39G3 : 92,000,000 miles, 
which is the distance of the sun from the earth. 

146. Velocity of the Eartl?s Motion in its Orbit. — Since 
the earth makes the entire circuit around the sun in one 
year, its daily motion may be found by dividing the cir- 
cumference of its orbit by 365-£, and thence we may find the 
motion for one hour, minute, or second. The circumference 
of the earth's orbit is 577,000,000 miles; whence we find 
that the earth moves 1,580,000 miles per day; 65,800 miles 
per hour; 1097 miles per minute; and 18 miles per second. 

By the diurnal rotation, a point on the earth's equator is 
carried round at the rate of 1037 miles per hour; hence the 
motion in the orbit is 63 times as rapid as the diurnal mo- 
tion at the equator. 

147. The Diameter of the Sun. — The sun's absolute di- 
Fig# 48 ameter can be computed 

when we know his dis- 
tance and apparent di- 
ameter. The apparent 
diameter at the mean 

distance is 32' 4". Hence we have the proportion, 

1 : sin. 16' 2" :: 92 millions (ES) : 428,000 miles, 

which is the sun's radius. Hence his diameter is 856,000 

miles. 




90 



ASTEOXOMT. 



The diameter of the sun is therefore 10? times that of the 
earth ; and, since spheres are as the cubes of their diame- 
ters, the volume of the sun is about 1,260.000 times that of 
the earth. 

The density of the sun is about one quarter that of the 
earth, and therefore his mass, which is equal to the product 
of his volume by his density, is found to be 318,000 times 
that of the earth. 

148. Forct tvity on the Sun. — Since the attraction 

of a sphere is proportional to its mass directly, and the 
square of the distance from the centre inversely, we can 
compute the ratio of the force of gravity on the surface of 
the sun to that on the earth, and we find the ratio to be 27 
to 1 ; that is, one pound of terrestrial matter at the sun's 
surface would exert a pressure equal to what 27 such pounds 
would do at the surface of the earth. 

At the surface of the earth, a body falls through 16 feet 
in one second ; but a body on the sun would fall through 
16 x 2 7, or 440 feet in one second. 



Fir.-:?. 



^ 













149. Solar Spots.— 

When we examine 
the sun with a good 
telescope, we c 
perceive upon his disc 
black spots of irreg- 
ular form, sometimes 
extremely minute, 
and at other times of 
extent. Their 
appearance is usual- 
ly that of an intei - - 
ly black, irregularly- 
shaped patch, called 
the ?i u sur- 

roun l fringe 

which is less dark, 
and is called the 
bra. The form 



SOLAR SPOTS. 91 

of this border is generally similar to that of the inclosed 
black spot ; but sometimes several dark spots are included 
within the same penumbra. 

Black spots have occasionally been seen without any pe- 
abra, and sometimes a large penumbra has been seen 
without any central black spot : but generally both the nu- 
clei;- mumbra are combined. 

The spots usually appear in clusters of from two or three 
up to fii ..ore. In one instance upward of 200 single 

spots and points were counted in a large group of spots. 

150. -^ I >f the Spots. — Solar spots are sometimes 

of immense magnitude, so that they have been repeatedly 
visible to the naked eye. Xot unfrequently they subtend 
an angle minute, which indicates a diameter ol'2C. 

miles. In 1543 a solar spot appeared which had a diameter 
, and remained for a whole week visible to 
the naked eye. A group of spots, with the penumbra sur- 
rounding it, has been observed, having a diameter of 147. 
mrilea 

151. 5L — The spot- ; their form 
from day to day. and sometimes from hour to hour. They 
usually commence from a point of insensible magnitude, 
grow very rapidly at first, and often attain their full size in 
less than a day. Then they remain nearly stationary, with 
a well-defined penumbra, and sometimes continue for weeks 
or even months. Then the nucleus usually I 

by a luminous line, which sends out numerous branches, un- 
til the entire nucleus is covered by the penumbra. 

Decided changes have been detected in the i uce 

of a spot within the interval of a single hour, indicating 
motion upon the sun's surface ol at U dies per 

hour. 

The duration of the spots is very A spot has 

wished in less than 24 Lours, while in an- 
r instance a spot remained for eight months. 

152. I — The number of spots seen 
on the sun's disc varies greatly in different years. Some- 



92 



ASTRONOMY. 



times the disc is entirely free from them, and continues thus 
for weeks or even months together; at other times a large 
portion of the sun's disc is covered with spots, and some 
years the sun's disc is never seen entirely free from them. 
From a long series of observations, it appears that the spots 
are subject to a certain periodicity. The number of the 
spots increases during 5 or 6 years, and then decreases dur- 
ing about an equal period of time, the interval between two 
consecutive maxima /being from 10 to 12 years. The last 
year of minimum was 1867. 

153. FaculoB. — Frequently we observe upon the sun's disc 
curved lines, or branching streaks of light, more luminous 
than the general body of the sun. These are called faculae. 
They generally appear in the neighborhood of the black 
spots. They are sometimes 40,000 miles in length, and 1000 
to 4000 miles in breadth. 

The faculse are ridges or masses of luminous matter ele- 
vated above the general level of the sun's surface. A bright 
streak of unusual size has been observed at the very edge 
of the sun's disc, and it was seen to project beyond the cir- 
cular contour of the disc, like a range of mountains. Their 
actual height could not have been less than 500 miles, and 
was probably over 1000 miles. 

1 54. General Appearance of the Surfs Disc. — Independ- 
ently of the dark spots, the luminous part of the sun's disc 
is not of uniform brightness. It exhibits inequalities of 
light, which present a coarsely mottled appearance. We 
often notice minute dark dots which appear to be in a state 
of change ; and we also notice the appearance of bright 
granules scattered irregularly over the entire disc of the 
sun, giving the disc a resemblance to the skin of an or- 
ange. Some observers have reported the sun's surface to be 
formed all over of long narrow filaments resembling willow 
leaves. 



155. Apparent Motion of the Spots. — When a spot is ob- 
served from day to day, it is found to change its apparent 
position on the sun's surface, moving from east to west. Oc« 



SOLAR SPOTS. 



93 



casionally a spot may be seen near the eastern limb of the 
sun ; it advances gradually toward the centre, passes be- 
yond it, and disappears near the western limb after an in- 
terval of about 14 days. After the lapse of another fort- 
night, if it remain as before, it will reappear upon the east- 
ern limb in nearly the same position as at first, and again 
cross the sun's disc as before, having taken 27d. 7h. in the 
entire revolution. 

To account for these phenomena, it is necessary to admit 
that the sun has a motion of rotation from west to east 
around an axis nearly perpendicular to the plane of the 
ecliptic, and that the spots are upon the surface of the sun. 
This supposition explains the changes which take place in 
the form of the more permanent spots during their passage 
across the disc. When a spot is first seen at the eastern 
limb, it appears as a narrow streak; as it advances toward 
the middle of the disc, its diameter from east to west in- 
creases ; and it again becomes reduced to a narrow line as 
it approaches the western limb. 

156. The Solar Spots are not Planetary Bodies. — Soon 
after the discovery of the solar spots, it was maintained 
that they were small planets revolving 
round the sun. It is evident, however, 
that they are at the surface of the sun, for 
if they were bodies revolving at some dis- 
tance from it, the time during which they 
would be seen on the sun's disc would be 
less than that occupied in the remainder 
of their revolution. Thus, let S represent 
the sun, E the earth, and let ABC repre- 
sent the path of an opaque body revolving 
about the sun. Then AB represents that 
part of the orbit in which the body would 
appear projected upon the sun's disc, and 
this is less than half the entire circumfer- 
ence; whereas the spot reappears on the 
opposite limb of the sun after an interval 
nearly equal to that required to pass across 
the disc. 




94 



ASTRONOMY. 



157, To determine the Time of the Sun's Rotation. — It is 
found that a spot employs about 27i days in passing from 
one limb of the sun around to the same limb again, and it is 
inferred that this apparent motion is caused by a rotation 
of the sun upon his axis. This is not, however, the precise 
period of the sun's rotation ; for during this interval the 
earth has advanced nearly 30 degrees in its orbit. Let 
AA'B represent the sun, and EE'D the orbit of the earth. 
Fig. 51. _JQL_ When the earth is at E, the visible 

disc of the sun is AA'B ; and if the 
earth was stationary at E, then the 
time required for a spot to move 
from the limb B round to the same 
point again would be the time of 
the sun's rotation. But while the 
spot has been performing its appar- 
ent revolution, the earth has ad- 
vanced in her orbit from E to E', 
and now the visible disc of the sun 
is A'B', so that the spot has performed more than a com- 
plete revolution during the time it has taken to move from 
the western limb to the western limb again. Since an ap- 
parent rotation of the sun takes place in 27i days, the num- 




ber of apparent rotations in a year will be — ^, or 13.4. 

But, in consequence of the motion of the earth about the 
sun, if the sun had no real rotation, it would in one year 
make an apparent rotation in a direction contrary to the 
motion of the earth. Hence, in one year, there must be 14.4 
real rotations of the sun, and the time of one real rotation is 

• — ? or 25.3 days, which is nearly two days less than the 

time of an apparent rotation. 

158. Absolute Motion of the Solar Spots. — The apparent 
motion of the spots can not be wholly explained by suppos- 
ing a rotation of the sun upon his axis, for the apparent time 
of revolution of some of the spots is much greater than that 
of others. In one instance, the time of the sun's rotation, as 
deduced from observations of a solar spot, was only 24d. 7h., 



SOLAR SPOTS. 95 

while in another case it amounted to 26d. 6h. This differ- 
ence can only be explained by admitting that the spots have 
a motion of their own relative to the sun's surface, just as 
our clouds have a motion relative to the earth's surface. 

The motion of the solar spots in latitude is very small, and 
this motion is sometimes directed toward the equator, but 
generally from the equator. The motion of the spots in lon- 
gitude is more decided. Spots near the sun's equator have 
an apparent movement of rotation more rapid than those at 
a distance from the equator. While at the equator the daily 
angular velocity of rotation is 865' (indicating a rotation in 
25 days), in lat. 20° the velocity is only 840', and in lat. 30° 
it is 816' (corresponding to a complete rotation in 26J days). 

159. Position of the Sun's Equator. — Besides the time of 
rotation, observations- of the solar spots enable us to ascer- 
tain the position of the sun's equator with reference to the 
ecliptic. The inclination of the sun's equator to the ecliptic 
has been determined to be about 7 degrees. About the first 
weeks of June and December, the spots, in traversing the 
sun's disc, appear to us to describe straight lines, but at oth- 
er periods of the year the apparent paths of the spots are 
somewhat curved, and they present the greatest curvature 
about the first weeks of March and September. 

160. Region of the Spots.— The spots do not appear with 
equal frequency upon every part of the sun's disc. With 
very few exceptions they are confined to a zone extending 
from 30° of N. latitude to 30° of S. latitude, measured from 
the sun's equator. There are only three cases on record in 
which spots have been seen as far as 45° from the sun's 
equator. Moreover, spots are seldom seen directly upon 
the sun's equator. They are most abundant near the paral- 
lel of 18 degrees in either hemisphere. 

161. The dark Spots are .Depressions below the luminous 
Surface of the Sun.— This was first proved by an observa- 
tion made by Dr. Wilson, of Glasgow, in 1 769. He noticed 
that as a large spot came near the western limb, the penum- 
bra on the eastern side, that is, on the side toward the centre 



96 ASTRONOMY. 

of the disc, contracted and disappeared, while on the other 
side the penumbra underwent but little change. This is 
shown indistinctly in Fig. 52, and more distinctly in Fig. 53. 

Fig. 52. 






21 



When the spot first reappeared on the sun's eastern limb, 

there was no penumbra on the western side, which was now 

Fig. 53. the side toward the centre of the disc, 

ej£2| p| although the penumbra was distinctly 

itWjf IE seen on the remaining sides. As the 

*mm- w$ S p £ advanced upon the disc, the pe- 

numbra came into view on the western side, though narrow- 
er than on the other sides. As the spot approached the mid- 
dle of the disc, the penumbra appeared of equal extent on 
every side of the nucleus. These observations prove that 
both the black nucleus and penumbra were below the lumi- 
nous surface of the sun. Dr. Wilson estimated the depth 
of the spot to be nearly 4000 miles. 

Similar observations have repeatedly been made by more 
recent astronomers. 

162. The Sun is not a solid Body. — That the outer enve- 
lope of the sun is not solid is proved by the rapid changes 
which take place upon its surface. We can hardly suppose 
a liquid body to move with a velocity of 1000 miles per 
hour, a rate of motion which has been observed in solar 
spots, Art. 151. We conclude, therefore, that the luminous 
matter which envelops the sun must be gaseous, or of the 



THK SUN'S PHOTOSPHERE. 97 

nature of a precipitate suspended in a gaseous medium, in a 
manner analogous to the clouds which are suspended in our 
own atmosphere. 

A comparison of the dark lines in the solar spectrum has 
shown that the most refractory substances, such as iron and 
nickel, exist upon the sun in a state of elastic vapor. The 
vast amount of heat received by the earth from the sun, at 
the distance of 92 millions of miles, proves that the heat of 
the sun must be very intense. These two considerations 
combined leave but little doubt that the heat of the sun far 
exceeds that of terrestrial volcanoes, a degree of heat w r hich 
is sufficient to melt any substance upon the earth. We can 
not, therefore, well suppose that any large part of the sun's 
mass is in the condition of a solid, or even a liquid body ; 
but it is probable that the principal part, if not the entire 
mass of the sun, consists of matter in the gaseous condition, 
or of matter in a state of minute subdivision suspended in a 
gaseous medium. 

163. Nature of the Swi* s Photosphere. — The bright enve- 
lope of the sun, which is the great source of the sun's light, 
is called the photosphere of the sun. This photosphere con- 
sists of matter in a state analogous to that of aqueous vapor 
in terrestrial clouds ; that is, in the condition of a precipitate 
suspended in a transparent atmosphere. By observations 
with the spectroscope, it is considered to be proved that the 
following substances (and probably many others) exist in 
the sun's photosphere, viz., iron, copper, zinc, nickel, sodium, 
magnesium, calcium, chromium, and barium. The sun's at- 
mosphere consists of the vapors of these substances, and the 
visible matter of the photosphere probably consists of parti- 
cles of these substances precipitated in consequence of their 
loss of heat by radiation. This does not imply that the pho- 
tosphere is not intensely hot, but simply that its heat is less 
than that of the interior of the sun. 

The sun's gaseous envelope extends far beyond the photo- 
sphere. During total eclipses we observe vast masses of a 
delicate lfeht rising to a height of 80,000 miles above the 
surface of the sun, which indicates the existence of bodies 
analogous to clouds floating at great elevations in an atmos 

E 



98 



ASTRONOMY. 



phere, and it is not improbable that the solar atmosphere 
extends to more than a million of miles beyond his surface. 

164. Nature of the Penumbra. — The penumbra of a solar 
spot appears to be formed of filaments of photospheric light 
converging toward the centre of the nucleus, each of the 
filaments having the same light as the photosphere, and the 
sombre tint results from the dark interstices (which are of 
the same nature as the dark nucleus) between the luminous 
streaks. The dark nucleus is simply a portion of the sun's 
gaseous mass not containing any sensible portion of the lu- 
minous precipitate, and therefore emitting but a very feeble 
light. The convergence of the luminous streaks of the pe- 
numbra toward the centre of the spot indicates the exist- 
ence of currents flowing toward the centre. These converg- 
ing currents probably meet an ascending current of the 
heated atmosphere, by contact with which the matter of the 
photosphere is dissolved and becomes non-luminous. 

165. Origin of the Surfs Sjjots. — The sun's spots exhibit 
a remarkable periodicity, and the principal period varies 
from 9 to 13 years, averaging a little more than 11 years. 
As this period corresponds to the time of one revolution of 
Jupiter, it is inferred that Jupiter has the power of sensibly 
disturbing the sun's photosphere. A careful discussion of 
all the reliable observations of the spots which have been re- 
corded has shown that Saturn and Venus also exert an ap- 
preciable influence upon the sun's photosphere. Such an 
effect can scarcely be ascribed to that force of attraction of 
the planets by which they are held in their orbits, but it is 
probably of a magnetic or electric origin. We may sup- 
pose that the matter of the sun's photosphere is in a mag- 
netized state, and that the action of the planets excites elec- 
tric currents in that region of the sun which is most direct- 
ly exposed to their influence; and that these electric cur- 
rents set in motion the solar atmosphere, causing movements 
analogous to the winds which prevail upon the earth. Ob- 
servations frequently indicate a tendency of the solar at- 
mosphere toward particular points. Such a movement must 
develop a tendency to revolve around this central point, for 



ZODIACAL LIGHT. 



99 







the same reason that terrestrial storms sometimes rotate 
about a vertical axis. A rotary motion of the solar spots 
has been repeatedly indicated by obser- 
vation. Moreover, sola r spots have 
sometimes exhibited a spiral structure 
such as might be supposed to result from 
rotation about a vertical axis. See Fig. 
54. 

The faculae are ascribed to commo- 
tions in the photosphere, by which the 
thickness of the phosphorescent stratum 
is rendered greater in some places than in others, and the 
surface appears brightest at those points where the lumin- 
ous envelope is the thickest 

166. Zodiacal L^jld. — The zodiacal light is a faint light, 
somewhat resembling that of the Milky Way, which is seen 
at certain seasons of the year in the west after the close of 
evening twilight, or in the east before the commencement 
of the morning twilight. Its apparent form is nearly tri- 
angular, with its base toward 
the sun, and its axis is situ- 
I nearly in the plane of 
the ecliptic. The season most 
favorable for observing this 
phenomenon is when its di- 
rection, or the direction of the 
ecliptic, is most nearly per- 
pendicular to the horizon. In 
northern latitudes this occurs 
in February and March for 
the evening, and in October 
and November for the morn- 
ing. 

e di-tance to which the 
zodiacal light extends from 
the sun varies with the sea- 
son of the year and the state 
of the atmosphere. It is sometimes more than 90 degrees, 
but ordinarily not more than 40 or 50 degrees. Its breadth 



Fig. 55. 




100 ASTRONOMY. 

at its base perpendicularly to its length varies from 8 to 30 
degrees. It is brightest in the parts nearest the sun, and in 
its upper part its light fades away by insensible degrees, so 
that different observers at the same time and place assign 
to it different limits. In tropical regions the zodiacal light 
has been seen at all hours of the night to extend entirely 
across the heavens, from the eastern to the western horizon, 
in the form of a pale luminous arch, having a breadth of 30 
degrees. 

167. Cause of the Zodiacal Light* — The zodiacal light is 
probably caused by an immense collection of extremely mi- 
nute bodies circulating round the sun in orbits like the plan- 
ets or comets. These bodies are too minute to be separate- 
ly visible even in our telescopes, but their number is so im- 
mense that their joint light is sufficient to produce a strong 
impression upon the eye. These bodies are crowded togeth- 
er most closely in the neighborhood of the sun, but they ex- 
tend beyond the orbits of Mercury and Venus, and in dimin- 
ished numbers even beyond the orbit of the earth. It is 
probable that shooting stars are but individuals of this group 
of bodies which the earth encounters in its annual motion 
around the sun. If the sun could be viewed from one of the 
other stars, it would probably appear to be surrounded by 
a nebulosity similar to that in which some of the fixed stars 
appear to be enveloped, as seen from the earth. 






ABERRATION OF LIGHT. 



101 



CHAPTER VL 

ABERRATION. — PRECESSION OF THE EQUINOXES. —NUTATION. 

168. Aberration of Light. — The motion of the earth in its 
orbit about the sun, combined with the progressive motion 
of light, causes the stars to appear in a direction different 
from their true direction. This apparent displacement of 
the star is called the aberration of the star. The nature of 
this phenomenon may be understood from the following il- 
lustration. 

Let us suppose a shower of rain to fall during a perfect 
calm, in which the drops descend in vertical lines. If the 
observer, standing still, hold in his hand a tube in a vertical 
position, a drop of rain may pass through the tube without 
touching the side. But if the observer move forward, the 
rain will strike against his face ; and in order that a drop 
of rain may descend through the tube without touching the 
side, the upper end of the tube must be inclined forward. 
3^ j^ g i Suppose, while a rain-drop is falling from 

/S' E to D with a uniform velocity, the ob- 
server moves from C to D, and carries 
the tube inclined in the direction EC. 
A drop of rain entering the tube at E, 
when the tube has the position EC, 
would reach the ground at D when the 
tube has come into the position FD ; 
and if the observer were unconscious 
of his own motion (as might happen 
upon a vessel at sea), the drop of rain 
would appear to fall in the oblique direction of the tube. 
Now, in the triangle CED, 

CD 
= ED ; 

that is, the tangent of the apparent deflection of the rain- 
drop = the velocity of the observer divided by the velocity 
of the falling drop. 




tan?. CED: 



102 



ASTRONOMY. 



169. Aberration of Light determined. — In like manner, the 
aberration of light is produced by the motion of the observ- 
er combined with the motion of light. Let AB represent a 
small portion of the earth's orbit about the sun, and let S be 
the position of a star. Let CD be the distance through 
which the earth moves in one second, and ED the distance 
traversed by light in the same time. Suppose that CE is 
the position of the axis of a telescope when the earth is at 
C, and that, as the earth moves from C to D, the tube re- 
mains parallel to itself, a ray of light from the star S, in mov- 
ing from E to D, will pass along the axis of the tube, and 
will arrive at D when the earth reaches the same point. 
The star will appear in the direction of the axis of the tele- 
scope ; that is, the star appears in the direction S'D, instead 
of its true direction, SD ; and the angle CED is the aberra- 
tion of the star. Now the velocity of the earth in its orbit 
is about 18 miles per second, while the velocity of light is 
185,000 miles per second, and 

tang. CED =- 18 . 

° 185,000 

Hence CED = 20"; that is, the aberration of a star which is 
90° from the direction in which the earth is moving, amounts 
to 20". 



170. Annual Curve of Aberration. — The effect of aberra- 
tion at any one time is to displace the star by a small amount 
directly toward that point of the ecliptic toward which the 
earth is moving. The position of this point varies with the 
season of the year, and in the course of a year this point will 
move entirely round the ecliptic ; that is, in consequence of 
aberration, a star appears to describe in the heavens a small 
curve around its true position. If the star be situated at 
the pole of the ecliptic, it will appear annually to describe 
about its true place a small circle whose radius is 20". 

If the star be situated in the plane of the ecliptic, then 
once during a year the earth and the light of the star will 
be moving in the same direction, and once during the year 
they will be moving in opposite directions, in both of which 
cases there will be no aberration. The aberration during 
the year will be alternately 20" upon one side of the true 



PRECESSION OF THE EQUINOXES. 103 

position of the star, and 20" upon the opposite side, but the 
star will always appear in the plane of the ecliptic. 

If the star be situated any where between the ecliptic and 
its poles, it will appear annually to describe an ellipse whose 
centre is the true place of the star. The major axis of the 
ellipse will be 40", but its minor axis will increase with its 
distance from the plane of the ecliptic. 

171 1 Fixed Position of the Ecliptic, — By comparing re- 
cent catalogues of stars with those formed centuries ago, we 
find that the latitudes of the stars continue very nearly the 
same. Now the latitude of a star is its angular distance 
from the ecliptic ; and since this distance is well-nigh invari- 
able, it follows that the plane of the ecliptic remains fixed, 
or nearly so, with reference to the fixed stars. 

172. Precession of the Equinoxes. It is found that the 
longitudes of all the stars increase at the same mean rate of 
about 50" in a year. Since this increase of longitude is com- 
mon to all the stars, and is nearly the same for each star, we 
can not ascribe it to motions in the stars themselves. It fol- 
lows, therefore, that the vernal equinox, the point from which 
longitude is reckoned, has an annual motion of about 50" 
along the ecliptic, in a direction contrary to the order of the 
signs, or from east to west. The autumnal equinox, being 
always distant 180° from the vernal, must have the same 
motion. This motion of the equinoctial points is called the 
precession of the equinoxes,hecai\se the place of the equinox 
among the stars each year precedes (with reference to the 
diurnal motion) the place which it had the previous year. 

The amount of precession is 50" annually. If we divide 
the number of seconds in the circumference of a circle by 
50, we shall find the number of years required for a complete 
revolution of the equinoctial points. This time is about 
25,000 years. 

173. Progressive Motion of the Pole of the Equator. — 
Since the ecliptic is stationary, it is evident that the earth's 
equator must change its position with reference to the stars, 
otherwise there would be no motion of the equinoctial points. 



104 



ASTRONOMY. 



Now a motion of the equator implies a motion of the poles 
of the equator; and since it appears from observation that 
the inclination of the equator to the ecliptic remains nearly 
constant, the distance from the pole of the equator to the 
pole of the ecliptic must remain nearly constant. Hence it 
appears that the pole of the equator has a motion about the 
pole of the ecliptic in a small circle whose radius is equal to 
the obliquity of the ecliptic, or about 23^ degrees. Its rate 
of motion must be the same as that of the equinox, or 50" 
annually, and the pole of the equator will accomplish a com- 
plete revolution in 25,000 years. 

1 74. Change of the Pole Star. — The pole of the equator, 
in its revolution about the pole of the ecliptic, must pass 
successively by different stars. At the time the first cata- 
logue of the stars was formed (about 2000 years ago), the 
north pole was nearly 12 degrees distant from the present 
pole star, while its distance is now less than 1-J degrees. The 
pole Avill continue to approach this star till the distance be- 
tween them is about half a degree, after which it will begin 
to recede from it. After the lapse of about 12,000 years, 
the pole will have arrived within about five degrees of the 
brightest star in the northern hemisphere, a star in the con- 
stellation Lyra. 

165. Effect of Precession on the Length of the Year. — 
The time occupied by the sun in moving from the vernal 
equinox to the vernal equinox again is called a tropical 
year. The time occupied by the sun in moving from one 
fixed star to the same fixed star again is called a sidereal 
year. 

On account of the precession of the equinoxes, the tropical 
year is less than the sidereal year, the vernal equinox hav- 
ing gone westward so as to meet the sun. The tropical 
year is less than the sidereal year by the time that the sun 
takes to move through 50" of its orbit. This amounts to 
20m. 22s. 

Since the mean length of a tropical year expressed in mean 
solar time is 365d. 5h. 48m. 48s., the length of the sidereal 
year is 365d. 6h. 9m. 10s. 



PRECESSION OF THE EQUINOXES. 105 

176. Signs of the Zodiac and Constellations of the Zodiac, 
— At the time of the formation of the first catalogue of stars 
(140 years before Christ), the signs of the ecliptic corre- 
sponded very nearly to the constellations of the zodiac bear- 
ing the same names. But in the interval of 2000 years since 
that period, the vernal equinox has retrograded about 28 
degrees, so that now the vernal equinox is near the begin- 
ning of the constellation Pisces ; the sign Taurus corresponds 
nearly with the constellation Aries; the sign Gemini with 
the constellation Taurus, and so for the others. 

177. Cause of the Precession of the Equinoxes. — The pre- 
cession of the equinoxes is caused by the action of the sun 
and moon upon that portion of the matter of the earth which 
lies on the outside of a sphere conceived to be described 
about the earth's axis. The earth may be considered as a 

Fig. 57. 




sphere surrounded by a spheroidal shell, thickest at -the 
equator, Art. 43. The matter of this shell may be regarded 
as forming around the earth a ring, situated in the plane of 
the equator. Now the tendency of the sun's action on this 
ring, except at the time of the equinoxes, is always to make 
it turn round the line of the eq*uinoxes toward the plane of 
the ecliptic, and the plane of the equator would ultimately 
coincide with that of the ecliptic were it not for the rota- 
tion of the earth upon its axis. The result of these two 
motions is that the axis of the earth is continually displaced, 
describing nearly the circumference of a circle about the 
pole of the ecliptic. 

178. Nutation. — The effect of the action of the sun and 

moon upon the earth's equatorial ring depends upon their 
position with regard to the equator, the effect being great- 
est when the distance of the body from the equator is great- 

E 2 



106 



ASTRONOMY. 



est. Twice a year, therefore, the effect of the sun to pro- 
duce precession is nothing, and twice a year it attains its 
maximum. The precession of the equinoxes, as well as the 
obliquity of the ecliptic, is therefore subject to a small semi- 
Fig. 53. annual variation, which is called the 
solar nutation. There is also a small 
inequality depending upon the posi- 
tion of the moon, which is called lunar 
nutation. In consequence of this os- 
cillatory motion of the equator, its 
pole, in revolving about the pole of 
the ecliptic, does not move strictly in 
a circle, but in a waving curve, as rep- 
resented in Fig. 58. 




DISTANCE AND DIAMETEK OF THE MOON. 10^ 



CHAPTER VTI. 

THE MOON — ITS MOTION. — PHASES. — TELESCOPIC APPEAR- 
ANCE. 

179. Definitions. — Two heavenly bodies are said to be in 
conjunction when their longitudes are the same ; they are 
said to be in opposition when their longitudes differ by 180 
degrees ; and they are said to be in quadrature when their 
longitudes differ 90 degrees or 270 degrees. The term syz- 
ygy is used to denote either conjunction or opposition. The 
octants are the four points midway between the syzygies 
and quadratures. 

The nodes of the moon's orbit or of a planet's orbit are 
the two points in which the orbit cuts the plane of the eclip- 
tic. The node at which the body passes from the south to 
the north side of the ecliptic is called the ascending node, 
and the other is called the descending node. 

180. Distance of the Moon. — The distance of the moon 
from the earth can be computed when we know its horizon- 
tal parallax. This parallax changes not only during one 
revolution, but also from one revolution to another, varying 
from 53' to 61'. Its mean value at the equator is 51' 2". 
Hence the mean distance will be found by the proportion 

sin. 51' 2": I :: 3963 : 239,000 miles, 
which is the average distance of the moon from the earth. 
This distance is, however, sometimes as great as 253,000 
miles, and sometimes as small as 221,000 miles. 

181. Diameter of the Moon. — The moon's absolute diam- 
eter can be computed when we know its distance and ap- 
parent diameter. The apparent diameter varies from 29' to 
33'; at the mean distance the apparent diameter is 31' 1'\ 
Hence the radius of the moon will be found by the propor- 
tion 1 : sin. 15' 33" :: 239,000: 1081 miles. 

The moon's diameter is therefore 2162 miles, 



108 ASTRONOMY. 

Since spheres are as the cubes of their diameters, the vol* 
ume of the moon is ^th that of the earth. Its density is 
about f ths the density of the earth, and therefore its mass 
(which is the product of the volume by the density) is about 
-g^th of the mass of the earth. 

182. Revolution of the Moon, — If we observe the situa- 
tion of the moon on successive nights, we shall find that it 
changes its position rapidly among the stars, moving among 
them from west to east ; that is, in a direction opposite to 
that of the diurnal motion. It thus makes a complete cir- 
cuit of the heavens in about 27 days. Hence either the 
moon revolves around the earth, or the earth round the 
moon ; or rather, according to the principles of Mechanics, 
we conclude that each must revolve about their common 
centre of gravity. This is a point in the line joining their 
centres, situated at an average distance of 2950 miles from 
the centre of the earth, or about 1000 miles beneath the sur- 
face of the earth. 

183. Sidereal and Synodic Revolutions. — A complete rev- 
olution of the moon about the earth occupies 27d. 711.43m., 
which is the time intervening between her departure from 
a fixed star and her return to it again. This is called the 
sidereal revolution. 

If we divide 360 degrees by the number of days in one 
revolution of the moon, we shall obtain the mean daily mo- 
tion, which is thus found to be a little more than 13 degrees. 

The synodical revolution of the moon is the interval be- 
tween two consecutive conjunctions or oppositions. The 
synodical revolution of the moon is more than two days 
longer than the sidereal, for this is the time required by the 
moon to describe the arc traversed by the sun since the pre- 
ceding conjunction. The synodical period is thus found to 
consist of 29d. 12h. 44m. 

184. ITovj the Sy?iodical Period is determined. — The mean 
synodical period may be determined with great accuracy by 
comparing recent observations of eclipses with those made 
in ancient times. The middle of an eclipse of the moon is 



OEBIT OF THE MOON. 109 

near the instant of opposition, and from the observations of 
the eclipse the exact time of opposition may be computed, 
Now eclipses have been very long observed, and we have 
the records of several which were observed before the com- 
mencement of the Christian era. By comparing the time 
of opposition deduced from these ancient observations with 
that of an opposition observed in modern times, and divid- 
ing this period by the number of intervening revolutions, 
we obtain the mean synodic period with great accuracy. 
When the synodic period has been determined, the sidereal 
period can be easily deduced from it. 

185. Form and Position of the Moon^s Orbit. — By observ- 
ing the moon from day to day when she passes the meridian, 
we find that her path does not coincide with the ecliptic, 
but is inclined to it at an angle a little greater than 5 de- 
grees, and intersects the ecliptic in two opposite points, which 
are called the moon's nodes. 

It can be proved in a manner similar to that employed 
for the sun, Arts. 107 and 110, that the moon, in her motion 
around the earth, obeys the following laws : 

1st. The moon's pathi3 an ellipse, of which the earth oc- 
cupies one of the foci. 

2d. The radius vector of the moon describes equal areas 
in equal times. 

That point in the moon's orbit which is nearest to the 
earth is called her perigee, and the point farthest from the 
earth her apogee. The line which joins the perigee and apo- 
gee is called the line of the apsides. 

The eccentricity of the moon's orbit may be determined 
by observing the moon's greatest and least apparent diam- 
eters, in the same manner as was done in the case of the 
sun, Art. 108. This eccentricity is more than three times as 
great as that of the earth's orbit, amounting to about y-g-th* 

186. Interval of 3fo oris Transits. — The moon's mean 
daily motion in right ascension is about 12 degrees greater 
than that of the sun. Hence if, on any given day, the moon 
should be on the meridian at the same instant with the sun, 
on the next day she will not arrive at the meridian till 51m. 



110 ASTRONOMY. 

after the sun; that is, the interval between two successive 
meridian passages of the moon averages 24h. 51m. This in- 
terval, however, varies from 24h. 38m. to 25h. 6m. 

187, Phases of the Moon. — The different forms which the 
moon's visible disc presents during a synodic revolution are 
called the phases of the moon. These phases are readily 
accounted for if we admit that the moon is an opaque glob- 
ular body, rendered visible by reflecting the light received 
from the sun. 

Let E represent the earth, ABCDH the orbit of the moon, 

Fig. 59, 



c 







and let the sun be supposed to be situated at a great dis- 
tance in the direction AS. Since the distance of the sun 
from the earth is about 400 times the distance of the moon, 
lines drawn from the sun to the different parts of the moon's 
orbit will be nearly parallel to each other. The moon be- 
ing an opaque globular body, that hemisphere which is turn- 
ed toward the sun will be continually illuminated, and the 
other will be dark. When the moon is in conjunction at A, 
the enlightened half is turned entirely away from the earth, 
and it is invisible. It is then said to be new moon. 

Soon after conjunction, a portion of the moon on the right 
begins to be seen, presenting the appearance of a crescent, 
with the horns turned from the sun, as represented at B. As 
the moon advances the crescent enlarges, and when the moon 
is in quadrature at C, one half of her illumined surface is 
turned toward the earth, and her enlightened disc appears 
as a semicircle. She is then said to be in her first quarter. 









PHASES OF THE MOON. Ill 

Soon after the first quarter, more than half the moon's 
disc becomes visible, as represented at D, and the moon is 
said to be gibbous. As the moon advances toward opposi- 
tion, the visible disc enlarges, and in opposition at F the 
whole of her illumined surface is turned toward the earth, 
and she appears as a full circle of light. It is then said to 
bo \full moon. 

From opposition to conjunction, the western limb will pass 
in the inverse order through the same variety of forms as 
the eastern limb in the interval between conjunction and 
opposition. When the moon is again in quadrature at H, 
one half of her illumined surface being turned toward the 
earth, she again appears as a semicircle. She is then said 
to be at her last quarter. These phases prove conclusively 
that the moon shines by light borrowed from the sun. 

The interval from one new moon to the next new moon is 
called a lunation, or lunar month. It is evidently the same 
as a synodical revolution of the moon. 

188, Obscure Part of the Moorts Disc. — When, after con- 
junction, the new moon first becomes visible, her entire disc 
is quite perceptible, the part which is not fully illumined ap- 
pearing with a faint light. As the moon advances, the ob- 
scure part becomes more faint, and before full moon it en- 
tirely disappears. This phenomenon depends on light of 
the sun reflected to the moon from the earth. 

When the moon is near to A, she receives light from near- 
ly an entire hemisphere of the earth, and this light renders 
that portion of the moon's disc which is not directly illu- 
mined by the sun faintly visible to us. As the moon ad- 
vances toward opposition at F, the amount of light she re- 
ceives from the earth decreases ; and its effect in rendering 
the obscure part visible is farther diminished by the in- 
creased light of that part which is directly illuminated by 
the sun's rays. 

It is obvious, therefore, that the earth, as viewed from 
the moon, goes through the same phases, in the course of 
a lunar month, as the moon does to an inhabitant of the 
earth; but its apparent diameter is more than three times 
as great. 



112 



ASTRONOMY. 



189. Harvest Moon. — Since the moon moves eastward 
from the sun about 12 degrees a day, it will rise (at a mean) 
about 50 minutes later each succeeding night ; but in the 
latitude of New York this interval varies in the course of a 
year from 23 minutes to lh. 17m. This retardation of the 
moon's rising attracts most attention when it occurs at the 
time of full moon. When the retardation is least, near the 
time of full moon, the moon for several successive evenings 
rises soon after sunset, before twilight is passed ; whereas, 
wdien the retardation is greatest, the moon in two or three 
days ceases to be seen in the early part of the evening. 

The reason of these variations is, that the arc (12°) through 
which the moon moves away from the sun in a day has 
very different inclinations to the horizon at different seasons 
of the year. In lat. 40°, this inclination varies from 21° to 
79°; and the interval of time employed in rising above the 
horizon will vary accordingly. Let HO represent the hori- 
zon, EQ the equator, and let AC, 
A'C represent two positions of 
the moon's orbit having the 
greatest and least inclinations to 
the horizon. Take BA, BA', each 
equal to 12°. The point A, by the 
diurnal motion, will be brought 
to the horizon after describing 
the arc AD parallel to the equa- 
tor, which may require less than 
30 minutes, while the point A' must describe the arc AD', 
which may require over 60 minutes. For the full moon this 
arc of 12° rises in the shortest time near the autumnal equi- 
nox. As this is about the period of the English harvest, 
this moon is hence called the Harvest Moon. 



Fig. 60. 




190. Moon's liotation vpon an Axis. — The moon always 
presents nearly the same hemisphere toward the earth, for 
the same spots always occupy nearly the same positions 
upon the disc. It follows, therefore, that the moon makes 
one rotation upon an axis in the same direction, and in the 
same time, in which she makes a revolution in her orbit. 
If the moon had no motion of rotation, then in opposite 



LIBRATIONS OF THE MOON. 113 

parts of her orbit she would present opposite sides to the 
earth. 

191. Librations of the Moon. — Although the spots on 
the moon's disc constantly occupy nearly the same situa- 
tions with respect to the visible disc, they are not exactly 
stationary, but alternately approach to and recede from the 
sdge of the disc. Those that are very near the edge some- 
times disappear, and afterward become visible again. This 
oscillatory motion of the moon's spots is called libration. 

Libration in Longitude. — While the moon's motion of ro- 
tation is perfectly uniform throughout the month, its angu- 
lar velocity in its orbit is not uniform, being most rapid 
w r hen nearest the earth. Hence small portions near the east- 
ern and western edges of the moon alternately come into 
view and disappear. The periodical oscillation of the spots 
in an east and w^est direction is called the libration in lon- 
gitude. 

Libration hi Latitude. — The moon's axis is not exactly 
perpendicular to the plane of her orbit, but makes an angle 
with it of 83-J- degrees, and remains continually parallel to 
itself. Hence the northern and southern poles of the moon 
incline 6^- degrees alternately to and from the earth. When 
the north pole leans toward the earth, we see beyond the 
north pole of the moon ; and when it leans the contrary 
way, w^e see beyond the south pole. This periodical oscil- 
lation of the spots in a north and south direction is called 
the libration in latitude. 

Diurnal Libration. — By the diurnal motion of the earth, 
we are carried with it round its axis ; and if the moon con- 
tinually presented the same hemisphere toward the earth's 
centre, the hemisphere visible to us when the moon is near 
the eastern horizon would be different from that which 
would be visible to us w T hen the moon is near the western 
horizon. This is another cause of a variation in the edges 
of the moon's disc, and is called the diurnal libration. 

In consequence of all these librations, we have an oppor- 
tunity to observe somewhat more than half of the surface 
of the moon; yet there remains about three sevenths of its 
surface which is always hidden from our view. 



I II 



AJSTRONOMY. 



Pkr.ei. 



192. Telescopic Appearance of the Moon. — When the 

moon is viewed with a, telescope, especially if near quadra- 
ture, the bounding line between the illumined and dark por- 
tions of the moon's surface is seen to be very irregular 

and sea-rated. On 

the dark part of the 
face, near the illn 
mined surface, wo 
often notice insula- 
ted bright spot s ; 

and on the illumined 
port ion we also find 
dark spots. These 
appearances change 
sensibly in a few 
hours. As tin 1 Light 
oi' the 4 sun advances 

upon the moon, the 
dark spots become 
bright ; and at full 
moon they all dis- 
appear, except that certain regions appear somewhat loss 

luminous than Others, It. is hence inferred that the moon's 

surface is diversified by mountains and valleys. Fig. 61 is a 
representation of a small portion of the moon's surface, as 

seen with a powerful telescope near the time of first quarter, 

193. Particular Phenomena described. — Near the bound- 
ing line between the illumined and dark portions of the 
moon's surface^ we frequently observe the following phe- 
nomena: A bright ring nearly oircular; within it, on the 

side 4 next the sun, a black circular segment; and without 
it, on the side opposite 4 to the 4 sun, a. black region with a. 

boundary quite jagged. NTear the centre of tin 4 circle we 

Sometimes notice 4 a bright spe>t, and a blaok stripe 4 e 4 \te 4 iul- 

ing from it e>ppe>site 4 to the sun. After a lew hours, the' 

black portions are 4 found te> have Contracted in ewtemt, and 
in a day or two entirely disappear. 

After about two weeks t luse 4 dark portions reappear, but 

on the 4 siele 4 e>ppe>sitc \o t hat on which the 4 y w e 4 re 4 be 4 fore 4 seHMi ; 







HEIGHT OF THE LUNAR MOUNTAINS. 
Pig. 62. 



115 




and tliey increase in length until they pass entirely within 
the dark portion of the moon. These appearances indicate 
the existence of a circular wall, rising above the general 
level of the moon's surface, and inclosing a large basin, from 
the middle of which rises a conical peak. Fig. 62 gives a 
magnified representation of the annular mountain Cassini. 

194. Height of the Lunar Mountains. — The height of a 
lunar mountain may be determined by measuring with a 
micrometer the length of its shadow, or the distance of its 
summit, when first illuminated, from the enlightened part 
of the disc. 

Let AFE be the illuminated hem- 
isphere of the moon, SA a ray of 
the sun touching the moon at A, 
and let BD be a mountain so ele- 
vated that its summit just reaches 
to the ray SAB, and is illumined, 
while the intervening space AB is 
dark. Let us suppose the earth to 
be in the direction of the diameter 
AE produced. Let the angle which AB subtends at the 
earth be measured with a micrometer ; then, since the dis- 
tance of the moon from the earth is known, the absolute 
length of AB can be computed. Then, in the right-angled 
triangle ABC, AC, the radius of the moon, is known, whence 
BC can be computed ; and subtracting AC from BC gives 
BD, the height of the mountain. 

If the earth is so situated that the line AB is not seen 







1 1 G ASTRONOMY. 

perpendicularly, since we know the relative positions of the 
sun and moon, we can determine the inclination at which 
AI> is seen, and hence the absolute length of AB. 

The greatest elevation of any lunar mountain which has 
been observed is 2:3,800 feet, and ten different mountains 
have been observed having elevations of 18,000 feet and up- 
ward. The altitude of these mountains has probably been 
determined as accurately as those of the highest mountains 
on the earth. 

195. Has the Moon an Atmosphere? — That there is no 
considerable atmosphere surrounding the moon is proved 
by the absence of any appreciable twilight. Upon the 
earth, twilight continues until the sun is 18 degrees below 
the horizon ; that is, day and night are separated by a belt 
1200 miles in breadth, in which the transition from light to 
darkness is not sudden, but gradual — the light fading away 
into the darkness by imperceptible gradations. This twi- 
light results from the reflection of light by our atmosphere; 
and it* the moon had an atmosphere, we should notice a 
gradual transition from the bright to the dark portions of 
the moon's surface. Such, however, is not the case. The 
boundary between the light and darkness, though irregular, 
is extremely well defined and sudden. Close to this bound- 
ary, the unillumincd portion of the moon appears well-nigh, 
if not entirely, as dark as any portion of the moon's unil- 
lumined surface. 

196. Argument from the Absence of Refraction. — The ab- 
sence of an appreciable atmosphere is also proved by the ab- 
sence of refraction when the moon passes between us and 
the distant stars; Cor when a star suffers occupation from 
the interposition of the moon between it and the observer, 
the duration of the occultation is the same as is computed 
without making any allowance for the refraction of a lunar 
atmosphere. 

Many thousand occult, 'it ions of stars by the moon have 
been observed, and no appreciable effect of refraction has 
ever been detected, from which it is inferred that this re- 
fraction can not be as large a quantity as 4" of arc. Now 



IS THERE WATEE UPON THE MOON? 117 

the earth's atmosphere, in like circumstances, would change 

the direction of a ray of light over 4000"; whence it is in- 
ferred that if the moon have an atmosphere, its density can 
not exceed one thousandth part of the density of our own. 
Such an atmosphere is more rare than that which remains 
under the receiver of the best air-pump when it lias reached 
its limit of exhaustion. 

Certain phenomena have, however, been observed, which 
are thought to indicate the presence of a limited atmos- 
phere upon the moon's surface. A faint light has some- 
times been perceived extending from the horns of the new 
moon a little distance into the dark part of the moon's disc. 
This is considered to be the moon's twilight, and indicates 
the existence of an atmosphere, which, however, we can not 
suppose to be sufficient to support a column of mercury 
more than -j—^-ths of an inch in height. 

197. Is there Water upon the Moon ? — There are upon the 
moon certain dusky and apparently level regions which 
were formerly supposed to be extensive sheets of water, but 
when the boundary of light and darkness falls upon these 
regions we detect with a good telescope black shadows, 
indicating the existence of permanent inequalities, which 
could not exist on a liquid surface. These regions are 
therefore concluded to be extensive plains, with only mod- 
erate elevations and depressions. These level regions occu- 
py about one third of the visible surface of the moon. Then; 
are therefore no seas nor other bodies of water upon the sur- 
face of the moon. Moreover, if there were any water (even 
the smallest quantity) on the moon's surface, a portion of it 
would rise in vapor, and form an atmosphere which would 
have an elastic force far exceeding youths of an inch of mer- 
cury. This argument also proves that there is no water on 
that side of the moon which we have never had an opportu- 
nity to observe. 

198. The Moorts Mountain Forms. — The mountainous 
formations of the moon may be divided into three classes. 

A. Isolated peaks, or sugar-loaf mountains, rising sudden- 
ly from plains nearly level, sometimes to a height of 4 or 5 



118 



ASTRONOMY. 



miles. Such peaks also frequently occur in the centres of 
circular plains. 

B. Ranges of mountains, extending in length two or three 
hundred miles, and sometimes rising to the height of from 
18,000 to 20,000 feet. Sometimes they run nearly in a 
straight line, and sometimes they form fragments of a ring. 

C. Circular formations, or mountain ranges approaching 
nearly to the form of circles, constitute the characteristic 
feature of the moon's surface, not less than three fifths of 
the moon's surface being studded with them. They have 
been subdivided into bulwark plains, ring mountains, and 
craters. 

Fig. 64. 




Bulwark plains are circular areas varying from 40 to 120 
miles in diameter, inclosed by a ring of mountain ridges, or 
several concentric ridges. The inclosed area is generally a 
plain, from which rise mountains of less height. 

Ring mountains vary from 10 to 50 miles in diameter, and 




LUNAR AND TERRESTRIAL VOLCANOES COMPARED. 119 

are generally more nearly circular in their form. Their in- 
ner declivity is always steep, and the inclosed area often in- 
cludes a central mountain. 

Craters are still smaller, and inclose a small area, contain- 
ing generally a central mound or peak. 

Fig. 64 gives a general view of the mountainous region in 
the southwest part of the moon's disc; and Fig. 65 gives a 
magnified representation of one of these ring mountains. 

199. Comparison 'with Terrestrial Volcanoes. — The circu- 
lar mountains of the moon bear an obvious analogy to the 
volcanic craters upon the earth. Figure 66 represents the 

Fi<r. 66. 




crater of Kilauea on one of the Sandwich Islands, which 
presents a basin three miles in diameter and 1000 feet deep. 
The volcanoes Vesuvius, iEtna, Teneriffe, and others, bear so 
strong a resemblance to the circular mountains of the moon, 
that it is now generally admitted that the lunar mountains 
are of volcanic origin. They differ, however, from terres- 
trial volcanoes in their enormous dimensions and immense 
number. This difference may be ascribed in part to the 
feeble attraction of the moon, since objects on the moon's 
surface weigh only one sixth what they would on the earth ; 
and partly to the continued action of rain and frost, by wmich 
the older volcanic craters upon the earth have been disinte- 



120 ASTRONOMY. 

grated and leveled, while upon the moon, where there are 
no such agencies, the oldest volcanoes have preserved their 
outlines as sharp as the more recent ones. 

200. Are the Lunar Volcanoes extinct? — It is certain that 
most of the lunar volcanoes are entirely extinct ; and it is 
doubted whether any signs of eruption have ever been no- 
ticed. Herschel observed on the dark portion of the moon 
three bright points, which he ascribed to volcanic fires ; but 
the same lights may be seen every month, and they are prob- 
ably to be ascribed to mountain peaks, which have an unusu- 
al power of reflecting the feeble light which is emitted by 
the earth. Two astronomers, who have studied the moon's 
surface with greater care than any one else, assert that they 
have never seen any thing that could authorize the conclu- 
sion that there are in the moon volcanoes now in a state of 
ignition. 

In 1866 it was announced that a small crater called Linne, 
5 miles in diameter, had suddenly disappeared, and that its 
place was occupied by an ill-defined white spot. Since that 
time, however, the crater has been distinctly seen, and it is 
now claimed that the cloudy appearance was due to the dis- 
turbing effect of our atmosphere, which effect is specially 
noticeable over this spot, on account of the absence of well- 
defined points upon which the eye can rest. 



CENTRAL FORCES. — KEPLER'S LAWS. 



121 



CHAPTER Vin. 

CENTRAL FORCES. — LAW OF GRAVITATION. 

201. Curvilinear Motion. — If a body at rest receive an 
impulse in any direction, and is not acted upon by any oth- 
er force, it will move in the direction of that impulse ; that 
is, in a straight line, and with a uniform rate of motion. A 
body must therefore continue forever in a state of rest, or 
in a state of uniform and rectilinear motion, if not disturbed 
by the action of an external force. Hence, if a body move 
in a curve line, there must be some force which at each in- 
stant deflects it from the rectilinear course which it tends 
to pursue in virtue of its inertia. We may then consider 
this motion in a curve line to arise from two forces : one a 
primitive impulse given to the body, which alone would 
have caused it to describe a straight line ; the other a de- 
flecting force, which continually urges the body toward some 
point out of the original line of motion. 

202. Kepler's Laics. — Before Newton's discovery of the 
law of universal gravitation, the paths in which the planets 
revolve about the sun had been ascertained by observation ; 
and the following laws, discovered by Kepler, and gener- 
ally called Kepler's laws, were known to be true : 

(1.) The radius vector of every planet describes about the 

su?i equal areas in equal times. 

Fig. 67. 53 c Thus, if ACF repre- 

sent the orbit of a plan- 
et about the sun,S, and 
ifAB,CD,EF,etc.,are 
the arcs described by 
the planet in equal 
times, as, for example, 
one day, then the areas 
SAB, SCD, SEF, etc., 

will all be equal to each other. 




122 



ASTRONOMY. 



Fig. G8. 



(2.) The orbit of every planet is an ellipse, of which the sun 
occupies one of the foci. 

(3.) The squares of the times of revolution of the planets 
are as the cubes of their mean distances from the sun, or of 
the semi-major axes of their orbits. 

From these facts, discovered by an examination of obser- 
vations, we may deduce the law of attractive force upon 
which they depend. 

203. When a body moves in a curve, acted on by a force 
tending to a fixed point, the areas which it describes by radii 
drawn to the centre of force are in a constant plane, and are 
proportional to the times. 

Let S be a fixed 
point, which is the 
centre of attraction; 
let the time be di- 
vided into short and 
equal portions, and 
in the first portion 
of time let the body 
describe AB. In the 
second portion of 
time, if no new force 
were to act upon the 
body, it would pro- 
ceed to c in the same 
straight line,describ- 
ing Be equal to AB. 
But when the body 
has arrived at B, let 
a force tending to 
the centre, S, act on it by a single instantaneous impulse, and 
compel the body to continue its motion along the line BC. 
Draw Cc parallel to BS, and at the end of the second por- 
tion of time the body will be found in C, in the same plane 
with the triangle ASB. Join SC ; and because SB and Cc 
are parallel, the triangle SBC will be equal to the triangle 
SBc, and therefore also to the triangle SAB, because Be is 
equal to AB. 




LAW OF VARIATION OF GRAVITY. 123 

In like manner, if a centripetal force toward S act im- 
pulsively at C, D, E, etc., at the end of equal successive por- 
tions of time, causing the body to describe the straight lines 
CD, DE, EF, etc., these lines will all lie in the same plane, 
and the triangles SCD, SDE, SEF will each be equal to SAB 
and SBC. Therefore these triangles will be described in 
equal times, and will be in a constant plane ; and we shall 
have 

polygon SADS : polygon SAFS : : time in AD : time in AF. 
Let now the number of the portions of time in AD, AF 
be augmented, and their magnitude be diminished in infini- 
tum, the perimeter ABCDEF ultimately becomes a curve 
line, and the force which acted impulsively at B, C, D, E, 
etc., becomes a force which acts continually at all points. 
Therefore, in this case also, we have 

the curvilinear area SADS : the curvilinear area SAFS 

: : the time in AD : the time in AF. 
Conversely, it may be proved in a similar manner that if 
a body moves in a curve line in a constant plane in such a 
manner that the areas described by the radius vector about 
a fixed point are proportional to the times, it is urged by an 
incessant force constantly directed toward that point- 
Now, by Kepler's first law, the radius vector of each planet 
describes about the sun equal areas in equal times; hence 
it follows that each planet is acted upon by a force which 
urges it continually toward the centre of the sun. We say 
therefore that the planets gravitate toward the sun, and the 
force which urges each planet toward the sun is called its 
gravity toward the sun, 

204. Law of Variation of Gravity, — It is proved in treat- 
ises on Mechanics that if a body describe an ellipse, being 
continually urged by a force directed toward the focus, the 
force by which it is urged must vary inversely as the square 
of the distance. But by Kepler's second law the planets de- 
scribe ellipses, having the sun at one of their foci, and by the 
preceding article each planet is acted upon by a force which 
urges it continually toward the sun; hence it follows that 
the force of gravity of each planet toward the sun varies in- 
versely as the square of its distance from the sun's centre. 



124 ASTRONOMY. 

205. Gravity operates on all the Planets alike. — It is 
proved in treatises on Mechanics that when several bodies 
revolve in ellipses about the same centre of force, if the 
squares of the periodic times vary as the cubes of the ma- 
jor axes, the force by which they are all drawn toward the 
centre must vary inversely as the square of the distance. 
Hence we conclude that the planets are solicited by a force 
of gravitation toward the sun, which varies from one planet 
to another inversely as the square of their distance. It is 
therefore one and the same force, modified only by distance 
from the sun, which causes all the planets to gravitate to- 
ward him, and retains them in their orbits. This force is 
conceived to be an attraction of the matter of the sun for 
the matter of the planets, and is called the solar attraction. 
This force extends infinitely in every direction, varying in- 
versely as the square of the distance. 

206. The Planets 'endowed ivith an attractive Force. — The 
motions of the satellites about their primary planets are 
found to be in conformity with Kepler's laws ; hence the 
planets which have satellites are endowed with an attract- 
ive force, which extends indefinitely, and varies inversely 
as the square of the distance. It is evident also that the 
satellites gravitate toward the sun in the same manner as 
their planets, for their relative motions about their primaries 
are the same as if the planets were at rest. 

The planets which have no satellites are endowed with a 
similar attractive force, as is proved by the disturbances 
which they cause in the motion of the other planets. 

207. The force that causes bodies to fall near the earth's 
surface, being diminished in proportion to the square of the 
distance from the earth's centre, is found at the distance 
of the moon to be exactly equal to the force which retains 
the moon in her orbit. 

Let E be the centre of the earth, A a point on its surface, 
and BC a part of the moon's orbit assumed to be circular. 
When the moon is at any point, B, in her orbit, she would 
move on in the direction of the line BD, a tangent to the or- 
bit at B, if she was not acted upon by some deflecting force. 



THEORY OF UNIVERSAL GRAVITATION. 



125 



Let F be her place in her orbit one sec* 
ond of time after she was at B, and let 
FG be drawn parallel to BD, and FH par- 
allel to EB. The line FH, or its equal 
BG, is the distance the moon has been 
drawn, during one second, from the tan- 
gent toward the earth at E. If we divide 
the circumference of the moon's orbit by 
the number of seconds in the time of one 
revolution, we shall have the length of 
the arc BF. Hence, by the principles of 
Geometry, we can compute BG, which is 
found to be y^th of an inch. 

Now at the earth's surface a body falls 
through 192 inches in the first second; and the distance of 
the moon is 60 times the earth's radius. At the distance of 
the moon, the force of the earth's attraction will be found 
by the proportion 

60 2 :1 2 :: 192:^11 inch, 
Avhich agrees with the distance above computed. 




208. The component Particles of the Planets attract each 
other. — The force of attraction of one body for another 
arises from the attraction of its individual particles. A large 
planet may be regarded as a collection of numerous smaller 
planets, and the attraction of the whole must be the result 
of the attraction of the component parts. Thus the gravi- 
tation of the earth toward the sun is the sum of the gravi- 
tation of each of its particles, and hence the force of gravity 
of each of the planets is proportional to the matter which it 
contains — that is, to its mass. Moreover, since the attrac- 
tion of the planets varies inversely as the square of the dis- 
tance, the force of every particle must also vary inversely 
as the square of the distance of the particles. 



209. Theory of Universal Gravitation. — It follows, then, 
as a necessary consequence from the general facts or laws 
discovered by Kepler, that all bodies mutually attract each 
other with forces varying directly as their quantities of mat- 
ter, and inversely as the squares of their distances. This 



126 



ASTRONOMY. 



principle is called the law of universal gravitation. It was 
first distinctly promulgated by Sir Isaac Newton, and hence 
is frequently called Newton's theory of universal gravita- 
tion. 



Fig. TO. 



210. All the Bodies of the Sola?' System move in Conic 
Sections, — It was demonstrated by Newton that if a body 
(a planet, for instance) is impelled by a projectile force, and 
is continually drawn toward the sun's centre by a force 
varying inversely as the square of the distance, and no oth- 
er forces act upon the body, the body will move in one of 
the following curves — a circle, an ellipse, a parabola, or an 
hyperbola. The particular form of the orbit will depend 
upon the direction and intensity of the projectile force. 

If we conceive F to 
be the centre of an 
attractive force, and 
a body at A to be pro- 
jected in a direction 
perpendicular to the 
line AF, then there 
is a certain velocity 
of projection which 
would cause the body 
to describe the circle 
ABC ; a greater ve- 
locity would cause it 
to describe the ellipse 
ADE, or the more eccentric ellipse AGH ; and if the veloc- 
ity of projection be sufficient, the body will describe the 
semi-parabola AKL. If the velocity of projection be still 
greater, the body will describe an hyperbola. The curve can 
not be a circle unless the body be projected in a direction 
perpendicular to AF, and also the velocity of projection 
must be neither greater nor less than one particular veloci- 
ty, determined by the distance AF and the mass of the 
central body. If it differs but little from this precise ve- 
locity (either greater or less), the body will move in an el- 
lipse ; but if the velocity be much greater, the body will 
move in a parabola or an hyperbola. 




MOTIONS OF PROJECTILES. 



127 



If the body be projected in a direction oblique to AF, 
and the velocity of projection be small, the body will move 
in an ellipse ; if the velocity be great, it may move in a 
parabola or an hyperbola, but not in a circle. 

If the body describe a circle, the sun will be in the centre 
of the circle. If it describe an ellipse, the sun will be, not in 
the centre of the ellipse, but in one of the foci. If the body de- 
scribe a parabola or an hyperbola, the sun will be in the focus. 

The planets describe about the sun ellipses which differ 
but little from circles. A few of the comets describe very 
elongated ellipses ; and nearly all the others whose orbits 
have been computed move in curves which can not be dis- 
tinguished from parabolas. There are two or three comets 
which are thought to move in hyperbolas. 



Fig. 71. 



211. Motions of Projectiles.- — The motions of projectiles 
are governed by the same laws as the motions of the plan- 
ets. If a body be projected from the top of a mountain in a 
horizontal direction, it is deflected by the attraction of the 
earth from the rectilinear path which it would otherwise 
have pursued, and made to describe a curve line which at 
length brings it to the earth's surface; and the greater the 
velocity of projection, the farther it will go before it reaches 
the earth's surface. We may therefore suppose the velocity 
to be so increased that it shall pass entirely round the earth 
without touching it. 

Let BCD represent the 
surface of the earth ; AB, 
AC, AD the curve lines 
which a body would de- 
scribe if projected hori- 
zontally from the top of 
a high mountain, with 
successively greater and 
greater velocities. If 
there were no air to offer 
resistance, and the veloci- 
ty were sufficiently great, 
the body would pass en- 
tirely round the earth, 




128 ASTRONOMY. 

and return to the point from which it was projected. Such 
a body would be a satellite revolving round the earth in an 
orbit whose radius is but little greater than the radius of 
the earth, and the time of one revolution would be one hour 
and twenty-five minutes. 

212. Modification of Kepler's TJiirdLaw. — Kepler's third 
law is strictly true only in the case of planets whose quan- 
tity of matter is inappreciable in comparison with that of 
the central body. In consequence of the action of the plan 
ets upon the sun, the time *of revolution depends upon the 
masses of the planets as well as their distances from the sun. 
Consequently, in comparing the orbits described by differ* 
ent planets round the sun, we must suppose the central force 
to be the attraction of a mass equal to the sum of the sun 
and planet. With this modification Kepler's third law be- 
comes rigorously true. 



ECLIPSES OF THE MOON. 



129 



CHAPTER IX. 

ECLIPSES OF THE MOON. — ECLIPSES OF THE SUN. 

213. Cause of Eclipses, — An eclipse of the sun is caused 
by the interposition of the moon between the sun and the 
earth. It can therefore only occur when the moon is in con- 
junction with the sun — that is, at the time of new moon. 
An eclipse of the mcon is caused by the interposition of the 
earth between the sun and moon. It can therefore only oc- 
cur when the moon is in opposition — that is, at the time of 
full moon. 



214. Why Eclipses do not occur every Month. — If the 
moon's orbit coincided with the plane of the ecliptic, there 
would be a solar eclipse at every new moon, since the moon 
would pass directly between the sun and earth; and there 
would be a lunar eclipse at every full moon, since the earth 
would be directly between the sun and moon. But since 
the moon's orbit is inclined to the ecliptic about five de- 
grees, an eclipse can only occur when the moon, at the time 
of new or full, is at one of its nodes, or very near it. At 
other times, the moon is too far north or south of the eclip- 
tic to cause an eclipse of the sun, or to be itself eclipsed. 

215. Form of the EartKs Shadow. — Since the sun is much 
larger than the earth, and both bodies are nearly spherical, 
the shadow of the earth must have the form of a cone, whose 
vertex lies in a direction opposite to that of the sun. Let AB 




F 2 



130 ASTRONOMY. 

represent the sun, and CD the earth, and let the tangent 
lines AC 3 BD, be drawn and produced to meet in F. The 
triangular space CFD will represent a section of the earth's 
shadow, and EF will be the axis of the shadow. If the tri 
angle AFS be supposed to revolve about the axis SF, the 
tangent CF will describe the convex surface of a cone with- 
in which the light of the sun is wholly intercepted by the 
earth, 

216. To fiiid the Length of the Earth? s Shadow. — In Fig. 
72, EFC or EFD represents half the angle of the cone of 
the earth's shadow. Now, by Geometry, B. I., Prop. 27, 
SEB=EFB+-EBF; that is, EFB=SEB-EBF; or half the 
angle of the cone of the earth's shadow is equal to the sun's 
apparent semi-diameter minus his horizontal parallax. Thus 
the angle EFD becomes known ; and in the right-angled tri- 
angle EFD, we know the side ED, the radius of the earth, 
and all the angles. Hence we can compute EF, the length 
of the earth's shadow. The length varies according to the 
distance of the sun from the earth ; but its mean length is 
856,000 miles, w^hich is more than three times the distance 
of the moon from the earth. 

217, Breadth of the Earth'' s Shadow. — In order to deter- 
mine the duration of an eclipse, we must know the breadth 
of the earth's shadow at the point where the moon crosses 
it. Let M'M" represent a portion of the moon's orbit. The 
angle MEH represents the apparent semi-diameter of the 
earth's shadow at the distance of the moon. Now, by Ge- 
ometry, B. I., Prop. 27, EHD=rMEH+HFE; that is, MEH 
=EHD— HFE. But EHD represents the moon's horizontal 
parallax, and HFE is the sun's semi-diameter minus his hor- 
izontal parallax, Art. 216. Therefore half the angle sub- 
tended by the section of the shadow is equal to the sum of 
the parallaxes of the sun and moon minus the sun's semi- 
diameter. The diameter of the shadow can therefore be 
computed, and we find it to be about three times the moon's 
diameter. The moon may therefore be totally eclipsed for 
as long a time as she requires to describe about twice her 
own diameter, or nearly two hours. Tte eclipse will begin 



ECLIPSES OF THE MOON. 131 

when the moon's disc at M' touches the earth's shadow, and 
the eclipse will end when the moon's disc touches the earth's 
shadow at M" 

218. Different kinds of Lunar Eclipses. — When a part, 
but not the whole of the moon, enters the earth's shadow, 
the eclipse is said to be partial ; when the entire disc of 
the moon enters into the earth's shadow, the eclipse is said 
to be total y and if the moon's centre should pass through 
the centre of the shadow, it would be called a central eclipse. 
It is probable, however, that a strictly central eclipse of the 
moon has never occurred. When the moon just touches the 
earth's shadow, but passes by it without entering it, the cir- 
cumstance is called an appulse. 

219, The Ear Ms Penumbra. — Long before the moon en- 
ters the cone of the earth's total shadow, the earth begins 
to intercept from it a jDortion of the sun's light, so that the 
light of the moon's surface experiences a gradual diminu- 
tion. This partial shadow is called the earth's p>enumbra. 
Its limits are determined by the tangent lines AD, BC pro- 



Fig. 73. 




duced. Throughout the space included between the lines 
CK and DL, light will be received from only a portion of 
the sun's disc. If a spectator were placed at L, he would 
see the entire disc of the sun ; but between L and the line 
DF he would see only a portion of the sun's surface, and 
the portion of the sun which was hidden would increase 
until he reached the line DF, while within the space DFC 
the sun would be entirely hidden from view. 

Fig. Y4 represents the dark shadow of the earth, sur- 
rounded by the penumbra, and the moon is represented in 



132 



ASTRONOMY. 



Fig. 74 




three different positions, viz., at the beginning, middle, and 
end of the eclipse. 

220. Effect of the Earth y s Atmosphere. — We have hitherto 
supposed the cone of the earth's shadow to be determined 
by lines drawn from the edge of the sun, and touching the 
earth's surface. It is, however, found by observation that 
the duration of an eclipse always exceeds the duration com- 
puted on this hypothesis. This fact is accounted for in part 
by supposing that those rays of the sun which pass near the 
surface of the earth are absorbed by the lower strata of the 
atmosphere; but we must also admit that those rays of the 
sun which enter the earth's atmosphere at such a distance 
from the surface as not to be absorbed are refracted toward 
the axis of the shadow, and are spread over the entire ex- 
tent of the geometrical shadow, thereby diminishing the 
darkness, but increasing the diameter of the shadow, and, 
consequently, the duration of the eclipse. 

In consequence of the gradual diminution of the moon's 
light as it enters the penumbra, it is difficult to determine 
with accuracy the instant when the moon enters the dark 
shadow ; and astronomers have differed as to the amount 
of correction which should be made for the effect of the 
earth's atmosphere. It is the practice, however, to increase 
the computed diameter of the shadow by -^th part, which 



ECLIPSES OF THE SUN. 133 

amounts to the same thing as increasing the earth's radius 
by G6 miles. 

221. Moon visible in the Earth's Shadow. — When the 
moon is totally immersed in the earth's shadow, she does 
not, unless on some rare occasions, become wholly invisible, 
but appears of a dull reddish hue, somewhat of the color of 
tarnished copper. This phenomenon results from the re- 
fraction of the sun's rays in passing through the earth's at- 
mosphere, as explained in Art. 220. Those rays from the 
sun which enter the earth's atmosphere, and are so far from 
the surface as not to be absorbed, are bent toward the axis 
of the shadow, and fall upon the moon, producing sufficient 
illumination to render the disc distinctly visible. 

ECLIPSES OF THE SUN. 

222. Moorfs Shadow cast upon the Earth — We may re- 
gard an eclipse of the sun as caused by the moon's shadow 
falling upon the earth. Wherever the dark shadow falls 
there will be a total eclipse, and wherever the penumbra 
falls there will be a partial eclipse. In order to discover 
the extent of the earth's surface over which an eclipse may 
occur, we must ascertain the length of the moon's shadow. 

223. Length of the Mooris Shadow. — We will suppose 
the moon to be in conjunction, and also at one of her nodes. 
Her centre will then be in the plane of the ecliptic, and in 
the straight line passing through the centres of the sun and 
earth. 

Let ASB be a section of the sun, KFL that of the earth, 

Fig. 75. 
A 




B 

and CMD that of the moon interposed directly "between 
them. Draw AC, BD, tangents to the sun and moon, and 
produce these lines to meet in V. Then V is the vertex 



134 ASTRONOMY. 

of the moon's shadow, and CVD represents the outline of a 
cone whose base is CD. Now, by Geometry, B. I., Prop. 27, 

SMB=MVB+MBV; 
hence M VB = SMB - MB V. 

But SMB, which is the sun's semi-diameter as seen from the 
moon, is ^-J-^th greater than the sun's semi-diameter as seen 
from the earth, because the distance of the moon from the 
earth is 4-0-0 th of its distance from the sun ; and therefore 
the value of SMB is easily determined. Also MBV, the 
angle which the moon's radius subtends at the sun, is to the 
angle which the earth's radius subtends at the sun (which is 
the sun's horizontal parallax) as the moon's radius to the 
earth's radius ; and thus the value of MBV can be deter- 
mined. 

We thus obtain the angle MVB, which is half the angle 
of the cone of the moon's shadow; and, knowing also the 
moon's diameter, we can compute MV, the length of the 
shadow. We thus find that when the moon is at her mean 
distance from the earth, her shadow will not quite reach to 
the earth's surface. But when the moon is nearest to us, 
and her shadow is the longest, the shadow extends 14,000 
miles beyond the earth's centre ; and there must be a total 
eclipse of the sun at all places within this shadow. 

224. Breadth of the Moorfs Shadoio at the Earth, — Hav- 
ing found the greatest length of the moon's shadow, its 
breadth at the surface of the earth is easily computed. 

In the triangle FEV, we know two sides, FE and EV, and 
the angle FVE ; we can therefore compute VFE. But the 
angle FEG = VFE + FVE. Hence we know the arc FG, and 
of course FH; and allowing 69 miles to a degree, we have 
the value of FH in miles. We thus find that the greatest 
breadth of the moon's shadow at the surface of the earth, 
when it falls perpendicularly on the surface, is 166 miles. 

225. Path of the Moorfs Shadoio. — The moon's shadow 
cast upon the earth is at each instant nearly a circle whose 
diameter may have any value from zero up to 166 miles; 
but, on account of the rapid motion of the moon, this shadow 
will travel along the earth's surface with a velocity of about 



ECLIPSES OF THE SUN. 



135 



2000 miles per hour, and will pass entirely across the earth 
in somewhat less than four hours. The path of the moon's 
shadow will therefore be a zone of several thousand miles 
in length, and only a few miles in breadth. The penumbra, 
or partial shadow of the moon, may have a breadth of near 
ly 5000 miles. 

226. Different Kinds of Eclipses of the Sun. — A partial 
eclipse of the sun is one in which a part, but not the whole 
of the sun, is obscured. A total eclipse is one in which the 
entire disc of the sun is obscured. It must occur at all 
those places on which the moon's total shadow falls. A 
central eclipse is one in which the axis of the moon's shadow, 
or the axis produced, passes through a given place. An an- 
nular eclipse is one in which the entire disc of the sun is ob- 
scured, except a narrow ring or annulus round the moon's 
dark body. 

Fig. 76. The apparent discs 

of the sun and moon, 
though nearly equal, are 
subject to small varia- 
tions 7 corresponding to 
their variations of dis- 
tance, in consequence 
of which the disc of the 
m oon sometimes ap- 
pears a little greater, 
and sometimes a little 
less than that of the 
sun. If the centres of 
the sun and moon coin- 
cide, and the disc of the 
moon be less than that of the sun, the moon will cover the 
central portion of the sun, but will leave uncovered a nar- 
tow ring, which appears like an illuminated border round the 
body of the moon, as shown in Fig. 76. This is called an 
annular eclipse. 

227. Duration of Eclijyses. — A total eclipse of the sun 
can not last at any one place more than eight minutes ; and 




136 



ASTRONOMY. 



it seldom lasts more than four or five minutes. An annular 
eclipse can not last at any one place more than twelve and 
a half minutes, and it seldom lasts more than six minutes. 
The entire duration of an eclipse at one place may exceed 
three hours. 

Since the apparent directions of the centres of the sun 
and moon vary with the position of the observer on the 
earth's surface, an eclipse which is total at one place may be 
partial at another, while at other places no eclipse whatever 
may occur. 



228. Number of Eclipses in a Year. — There can not be 
less than two eclipses in a year, nor more than seven. The 
most usual number is four, and it is rare to have more than 
six. When there are seven eclipses in a year, five are of 
the sun and two of the moon ; when there are but two, they 
are both of the sun. In the year 1868 there were but two 
eclipses, while in 1823 there were seven. In 1869, August 
7th, the sun was totally eclipsed in Illinois, Kentucky, and 
North Carolina. 

Although the absolute number of solar eclipses is greater 
than that of lunar eclipses, yet at any given place more lunar 
than solar eclipses are seen, because a lunar eclipse is visi- 
ble to an entire hemisphere of the earth, while a solar is 
only visible to a part. 

229. Darkness attending a Total Eclipse of the Sun. — 
During a total eclipse the darkness is somewhat less than 
that which prevails at night in presence of a full moon, but 
the darkness appears much greater than this, on account of 
the sudden transition from day to night. This darkness is 
attended by an unnatural gloom, which is tinged with un- 
usual colors, such as a light olive, purple, or violet. 

230. The Corona. — When the body of the sun is concealed 
from view, the disc of the moon appears surrounded by a 
ring of light called the corona. It is brightest next to the 
moon's limb, and gradually decreases in lustre until it be- 
comes undistinguishable from the general light of the sky. 
Its apparent breadth is generally about one third of the 






ECLIPSES OF THE SUN. 



137 



Fi<?. 



moon's diameter, but 
sometimes is equal to the 
entire diameter of the 
moon. Its color is some- 
times white, sometimes 
of a pale yellow, and 
sometimes of a rosy tint. 
The intensity of its light 
is about equal to that of 
the moon. 

The corona generally 
presents somewhat of a 
radiated appearance. 
Sometimes these rays are 
very strongly marked, 

and extend to a distance greater than the diameter of the 

sun. 




231. Rose-colored Protuberances. — Immediately after the 
commencement of the total obscuration, red protuberances, 
resembling flames, are seen to issue from behind the moon's 
disc. They have various forms, sometimes resembling the 
tops of an irregular range of hills ; sometimes they appear 
entirely detached from the moon's limb, and frequently they 
extend in irregular forms far beyond the support of the base. 

Sometimes they rise to a height of 80,000 miles ; while 
others have every intermediate elevation down to the small- 
est visible object. They are generally tinged with red light, 
but sometimes appear nearly white, and sometimes they are 
so conspicuous as to be seen without a telescope. 

232. These Protuberances emanate from the Sun. — That 
these protuberances emanate from the sun, and not from the 
moon, is proved by the following observations. In the prog- 
ress of a total eclipse, the protuberances seen on the eastern 
limb continually decrease in their apparent dimensions, 
while those on the western limb continually increase in their 
dimensions, indicating that the moon covers more and more 
the protuberances on the eastern side, and gradually ex- 
poses more and more those on the western side. The pro- 



138 



ASTRONOMY. 



tuberances retain a fixed position with reference to the sun 
during the entire eclipse, and only change their form as the 
moon, by passing over them, shuts them off on the eastern 
side, while fresh ones become visible on the western. 

Fig. 78 is a representation of the solar eclipse of 1860, 
taken one minute after the commencement of total obscura- 
tion ; and Fig. 79 is a representation of the same eclipse, 



Fig. 78. 



Fisr. T9. 




taken just previous to the reappearance of the sun. In the 
first figure the luminous protuberances are chiefly on the 
left-hand side of the sun's disc, while in the second figure 
they are chiefly on the right-hand side. 

233. Nature of these Protuberances. — That these protuber- 
ances are not solid bodies like mountains is proved by their 
forms, as they sometimes appear without any visible sup- 
port; and the same consideration proves that they are not 
liquid bodies. They seem to be analogous to the clouds 
which float at great elevations in our own atmosphere ; and 
we are led to infer that the sun is surrounded by a transpar- 
ent atmosphere, rising to a height of a million of miles or 
more; and in this atmosphere there are frequently found 
cloudy masses of extreme tenuity floating at various eleva- 
tions, and sometimes rising to the height of 80,000 miles 
above the photosphere of the sun. 

234. Cause of the Corona. — The corona is probably due 



ECLIPSES OF THE SUN. 139 

to the solar atmosphere reflecting a portion of the sun's 
light. Its radiated appearance may result from a partial 
interception of the sun's light by clouds floating in his at- 
mosphere. These clouds, whose existence was shown in Art. 
233, would intercept a portion of the sun's light, and the 
space behind these would appear less bright than that por- 
tion of space which is illumined by the unobstructed rays 
of the sun. 

235. Occultations. — When the moon passes between the 
earth and a star or planet, she must render that body invisi- 
ble to some parts of the earth. This phenomenon is called 
an occultation of the star or planet. The moon in her 
monthly course occults every star which is included in a 
zone extending a quarter of a degree on each side of the 
apparent path of her centre. From new moon to full, the 
moon moves with the dark edge foremost ; and from full 
moon to new, it moves with the illuminated edge foremost. 
During the former interval, stars disappear at the dark edge, 
and reappear at the bright edge; while during the latter 
period they disappear at the bright edge, and reappear at 
the dark edge. The occultation of a star at the dark limb 
is extremely striking, inasmuch as the star seems to be in- 
stantly extinguished at a point of the sky w^here there is ap- 
parently nothing to interfere with it. 



140 ASTRONOMY. 



CHAPTER X. 

METIIODvS OF FINDING THE LONGITUDE OF A PLACE, 

236. Difference of Time under different Meridians.— 
Mean noon at any place occurs when the mean sun (Art. 
117) is on the meridian of that place. Now the sun, in his 
apparent diurnal motion from east to west, passes succes- 
sively over the meridians of different places, and noon oc- 
curs later and later as we travel westward from any given 
meridian. The sun will cross the meridian of a place 15° 
west of Greenwich one hour later than it crosses the Green- 
wich meridian — that is, at one o'clock of Greenwich time. 
A difference of longitude of 15° corresponds to a difference 
of one hour in local times ; and the difference of longitude 
of two places is the difference of their local times. In order, 
then, to determine the longitude of any place from Green- 
wich, we must accurately determine the local time, and com- 
pare this with the corresponding Greenwich time. 

237. Longitude by Artificial Signals, — The difference of 

the local times of two places may be determined by means 
of any signal which can be seen at both places at the same 
instant, When the places are not very distant from each 
other, the Hash of gunpowder, or the explosion of a rocket, 
may serve this purpose. By employing a sufficient number 
of intermediate stations, the difference of longitude of dis- 
tant places may be determined in this manner. 

238. Longitude by Chronometers. — Let a chronometer 
which keeps accurate time be carefully adjusted to the time 
of some place whose longitude is known — for example 4 , 
Greenwich Observatory. Then let the chronometer be car- 
ried to a, place whose longitude is required, and compared 
with the correct local time of that place. The difference 
between this time and that shown by the chronometer will 



METHODS OF FINDING THE LONGITUDE. 141 

be the difference of longitude between the given place and 
Greenwich. 

It is not necessary that the chronometer should be regu- 
lated so as neither to gain nor lose time. This would be 
difficult, if not impracticable. It is necessary, however, that 
its error and rate should be well determined, and an allow- 
ance can then be made for its gain or loss during the time 
of its transportation from one place to the other. 

The manufacture of chronometers has attained to such a 
degree of perfection that this method of determining differ- 
ence of longitude, especially of stations not very remote from 
each other, is one of the best methods known. When great 
accuracy is required, it is customary to employ a large num- 
ber of chronometers as checks upon each other; and the 
chronometers are transported back and forth a considerable 
number of times. 

This is the method by which the mariner commonly de- 
termines his position at sea. Every day, when practicable, 
he measures the sun's altitude at noon, and hence deter- 
mines his latitude, Art. 112. About three hours before or 
after noon he also measures the sun's altitude, and from this 
he computes his local time by Art. 123. The chronometer 
which he carries with him shows him the true time at Green- 
wich, and the difference between the two times is his longi- 
tude from Greenwich. 

239. Longitude by Lunar Eclipses. — An eclipse of the 
moon is seen at the same instant of absolute time in all 
parts of the earth where the eclipse is visible. Therefore, 
if at two distant places the times of the beginning of the 
eclipse are carefully observed, the difference of these times 
will be the difference of longitude between the places of ob- 
servation ; but, on account of the gradually increasing dark- 
ness of the penumbra, it is impossible to assign the precise 
instant when the eclipse begins, and therefore this method 
is of no value except under circumstances which preclude 
the use of better methods. 

The eclipses of Jupiter's satellites afford a similar method 
of determining difference of longitude, but it is attended 
with the same inconvenience as that of lunar eclipses. 



142 ASTROJNOMY. 

240. Longitude by Solar Eclipses, — The absolute times 
of the beginning and end of an eclipse of the sun are not 
the same for all places upon the earth's surface. We can 
not, therefore, use a solar eclipse as an instantaneous signal 
for comparing directly the local times at the two stations, 
but from the observed beginning and end of an eclipse we 
may by computation deduce the time of conjunction as it 
would appear if it could be seen from the centre of the earth ; 
and this is a phenomenon which happens at the same abso- 
lute instant for every observer on the earth's surface. If 
the eclipse has been observed under two different meridians, 
we may determine the instant of true conjunction from the 
observations at each station ; and since the absolute instant 
is the same for both places, the difference of the results thus 
obtained is the difference of longitude of the two stations. 
This is one of the most accurate methods known to astron- 
omers for determining the difference of longitude of two 
stations remote from each other. 

An occultation of a star by the moon affords a similar 
method of determining difference of longitude, and these oc- 
cupations are of far more frequent occurrence than solar 
eclipses. 

241. Longitude by the Electric Telegraph. — The electric 
telegraph affords the most accurate method of determining 
difference of longitude. By this means we are able to trans- 
mit signals to a distance of a thousand miles or more with 
almost no appreciable loss of time. Suppose there are two 
observatories at a great distance from each other, and that 
each is provided with a good clock, and with a transit in- 
strument for determining its error; then, if they are con- 
nected by a telegraph wire, they have the means of trans- 
mitting signals at pleasure to and fro for the purpose of 
comparing their local times. For convenience, we will cal) 
the most eastern station E, and the western W. 

A plan of operations having been previously agreed upon, 
the astronomer at E strikes the key of his register, and 
makes a record of the time according to his observatory 
clock. Simultaneously with this signal at E, the armature 
of the magnet at W is moved, producing a click like the 



METHODS OF FINDING THE LONGITUDE. 143 

ticking of a watch. The astronomer at W hears the sound 
and notes the instant by his clock. The difference between 
the time recorded at E and that at W is the difference be- 
tween the two clocks. A single good comparison in this 
way will furnish the difference of longitude to the nearest 
second ; but to obtain the greatest precision, the signals are 
repeated many times at intervals of ten seconds. 

The astronomer at W then transmits a series of signals to 
E in the same manner, and the times are recorded at both 
stations. By this double set of signals we obtain an ex- 
tremely accurate comparison of the two clocks. 

242. Hoto a Clock may break the Electric Circuit. — The 
most accurate method of determining difference of longitude 
consists in employing one of the clocks to break the electric 
circuit each second. This may be accomplished in the fol- 
lowing manner: Near the lower extremity of the pendulum 
place a small metallic cup containing a globule of mercury, 
so that once in every vibration the pointer at the end of the 
pendulum may pass through the mercury. A wire from one 
pole of the battery is connected with the supports of the 
pendulum, while another wire from the other pole of the 
battery connects with the cup of mercury. When the point- 
er is in the mercury, the electric circuit will be complete 
through the pendulum ; but as soon as it passes out of the 
mercury, the circuit will be broken. When the connections 
are properly made, there will be heard a click of the mag- 
net at each station simultaneously with the beats of the elec- 
tric clock. If each station be furnished with a proper regis- 
tering apparatus, there will be traced upon a sheet of paper 
a series of lines of equal length, separated by breaks, as 
shown in Fig. 80. The mode of using the register for mark- 
Fig. 80. 

-A. R f 

6* 7* s* 3 s 10 s 11 s n* - a s iF is 9 16 s 
ing the date of any event is to strike the key of the register 
at the required instant, when a break will be made in one of 
the lines of the graduated scale, as shown at A, B, and C, 
and the position of this break will indicate not only the sec- 
ond, but the fraction of a second at which the signal was made, 



144 ASTRONOMY. 

243. Transits of Stars Telegraphed. — We now employ 
the electric circuit for telegraphing the passages of a star 
across the wires of a transit instrument. A list of stars 
having been selected beforehand, and furnished to each ob- 
server, the astronomer at E points his transit telescope upon 
one of the stars as it is passing his meridian, and strikes the 
key of his register at the instant the star passes successively 
each wire of his transit, and the instants are recorded not 
only upon his own register, but also upon that at W. When 
the same star reaches the meridian of W, the observer there 
repeats the same operations, and his observations are print- 
ed upon both registers. 

These observations furnish the difference of longitude of 
the two stations, independently of any error in the tabular 
place of the star employed, and also independently of the 
absolute error of the clock. 

The transits of a considerable number of stars are ob- 
served in the same manner, and the observations may be va- 
ried by introducing into the circuit the clocks at the two 
stations alternately. By this method have been determined 
the longitudes of the principal stations along the entire Ac^ 
Ian tic coast of the United States. 









THE TIDES. 145 



CHAPTER XL 

THE TIDES. 

244. Definitions,— The alternate rise and fall of the sur- 
face of the ocean twice in the course of a lunar day, or about 
25 hours, is the phenomenon known by the name of tne tides. 
When the water is rising it is said to he flood tide, and when 
it reaches the highest point it is called high water. When 
the water is falling it is called ebb tide, and when it reaches: 
the lowest point it is called low water. 

245. Time of High Water. — The interval between one 
high water and the next is, at a mean, 12h. 25m. The time 
of high water is mainly dependent upon the position of the 
moon, and, for any given place, always occurs about the 
same length of time after the moon's passage over the me- 
ridian. This interval is very different at different places, 
being at some places two or three hours, while at others it 
is six, nine, or twelve hours. 

246. Height of the Tide. — The height of high water is 
not always the same at the same place, but varies from day 
to day, and these variations depend upon the phases of the 
moon, Near the time of new and full moon the tides are 
the highest, and these are called the spring tides. Near the 
quadratures, or when the moon is 90° distant from the sun, 
the tides are the least, and these are called the neap tides. 
At New York the average height of the spring tides is 5.4 
feet, and of the neap tides 3.4 feet, which numbers are near- 
ly in the ratio of 3 to 2. 

247. Tides affected by MoorCs Distance, etc. — The height 
of the tide is affected by the distance of the moon from 
the earth, being highest near the time when the moon is in 
perigee, and lowest near the time when she is in apogee. 
Unusually high tides will therefore occur when the time of 
new or fill moon coincides with the time of perigee. 

G 



146 



ASTRONOMY. 



The tides are also sensibly affected by the declinations of 
the sun and moon. 



248. Cause of the Tides. — The facts just stated indicate 
that the moon has some agency in producing the tides. It is 
not, however, the whole attractive force of the moon which 
is effective in raising a tide, but the difference of its attrac- 
tion upon the different particles of the earth's mass. Let 
ACEG represent the earth, and let us suppose its entire sur- 




Fig. 81. 



M 



face to be covered with water ; also let M be the place of 
the moon. The different parts of the earth's surface are at 
unequal distances from the moon. Hence the attraction 
which the moon exerts upon a particle at A is greater than 
that which it exerts at B and H, and still greater than that 
which it exerts at C and G, while the attraction which it ex- 
erts at E is least of all. The attraction which the moon ex- 
erts upon the mass of water immediately under it, near the 
point Z, is greater than that which it exerts upon the solid 
mass of the earth. The water will therefore be heaped up 
over A, forming a convex protuberance; that is, high water 
will take place immediately under the moon. The water 
which thus collects at A will flow from the regions C and G, 
where the quantity of water must therefore be diminished ; 
that is, there will be low water at C and G. 

The water at N is less attracted than the solid mass of the 
earth. The solid mass of the earth will therefore be drawn 
away from the waters at N ; that is, it will leave the water 
behind, which will thus be heaped up at N, forming a con- 
vex protuberance, or high water similar to that at Z. The 
water of the ocean is therefore drawn out into an ellipsoidal 
form, having its major axis directed toward the moon. 



THE TIDES. 147 

249. Effect of the Suri*s Attraction. — The attraction of 
the sun raises a tide wave similar to the lunar tide wave, 
but of less height, because, on account of its greater distance, 
the inequality of the sun's attraction on different parts of 
the earth is very small. It has been computed that the 
tidal wave due to the action of the moon is about double 
that which is due to the sun. 

There is therefore a solar as well as a lunar tide wave, the 
latter being greater than the former, and each following the 
luminary from which it takes its name. When the sun and 
moon are both on the same side of the earth, or on opposite 
sides — that is, when it is either new or full moon — both bod- 
ies tend to produce high water at the same place, and the re- 
sult is an unusually high tide, called spring tide. 

When the moon is in quadrature, the action of the sun 
tends to produce low water where that of the moon pro- 
duces high water, and the result is an unusually small tide, 
called neap tide. 

250. Effect of the Moorf s Declination on the Tides. — The 
height of the tide at a given place is influenced by the dis- 
tance of the moon from the equator. When the moon is 
upon the equator, the highest tides should occur along the 
equator, and the heights should diminish from thence both 
toward the north and the south ; but the two daily tides at 
any place should have the same height. When the moon 
has north declination, the highest tides on the side of the 
earth next the moon will be at places having a correspond- 
ing north latitude ; and of the two daily tides at any place, 
that which occurs when the moon is nearest the zenith should 
be the greatest. This phenomenon is called the diurnal in- 
equality, and in some places constitutes the most remarka- 
ble peculiarity of the tides. 

251. Nature of the Tide Wave. — The great wave which 
constitutes the tide is to be regarded as an undulation of 
the waters of the ocean, in which (except where it passes 
over shallows or approaches the shore) there is but little 
progressive motion of the water. This wave, if left undis- 
turbed, would travel with a velocity depending upon tha 



148 ASTKOiNOMT: 

depth of water. In water whose depth is 25 feet, the ve« 
locity of the wave should be 19 miles per hour, while in wa- 
ter whose depth is 50,000 feet, or nearly ten miles, its veloci- 
ty should be 865 miles per hour. 

252. Why the Phenomena of the Tides are so compli- 
cated. — The actual phenomena of the tides are far more 
complicated than they would be if the earth were entirely 
covered with an ocean of great depth. Two vast continents 
extend from near the north pole to a great distance south 
of the equator, thus interrupting the regular progress of the 
tidal wave across the globe. In the northern hemisphere 
the waters of the Atlantic communicate with those of the 
Pacific only by a narrow channel too small to allow the 
transmission of any considerable wave, while in the south- 
ern hemisphere the only communication is between Cape 
Horn and the Antarctic Continent. Through this opening 
the motion of the tidal wave is eastward, and not west- 
ward ; from which we see that the tides of the Atlantic are 
not propagated into the Pacific. 

253. Cotidal Lines. — The phenomena of the tides being 
thus exceedingly complicated must be learned chiefly from 
observations ; and in order to present the results of obser- 
vations most conveniently upon a map, we draw a line con- 
necting all those places which have high water at the same 
instant of absolute time. Such lines are called cotidal lines. 
Charts have been constructed showing the cotidal lines of 
nearly every ocean at intervals of lh., 2h., 3h., etc., after 
the meridian transit of the moon at Greenwich. 

254. Origin and Progress of the Tidal Wave. — By inspect- 
ing a chart of cotidal lines, we perceive that the great tidal 
wave originates in the Pacific Ocean, not far from the west- 
ern coast of South America, in which region high water oc- 
curs about two hours after the moon has passed the meridian. 
This wave travels toward the northwest, through the deep 
water of the Pacific, at the rate of 850 miles per hour. The 
same wave travels westward and southwestward at the rate 
of about 400 miles per hour, reaching New Zealand in a^b^ul 



THE TIDES. 149 

12 hours. Passing south of Australia, it travels westward 
and northward into the Indian Ocean, and is 29 hours old 
when it reaches the Cape of Good Hope. Hence it is propa- 
gated through the Atlantic Ocean, traveling northward at 
the rate of about 700 miles per hour, and in 40 hours from 
its first formation it reaches the shallow waters of the coast 
of the United States, whence it is propagated into all the 
bays and inlets of the coast. 

A portion of the great Atlantic wave advances up Baffin's 
Bay, but the principal part of it turns eastward, and in 44 
hours brings high water to the western coast of Ireland. 
After passing Scotland, a portion of this wave turns south- 
ward with diminished velocity into the North Sea, and 
thence follows up the Thames, bringing high water to Lon- 
don at the end of 66 hours from the first formation of this 
wave in the Pacific Ocean. 

255. Velocity of the Tidal Wave in Shallow Water. — As 
the tidal wave approaches the shallow water of the coast, 
its velocity is speedily reduced from 500 or perhaps 900 
miles per hour, to 100 miles, and soon to 30 miles per hour; 
and in ascending bays and rivers its velocity becomes still 
less. From the entrance of Chesapeake Bay to Baltimore 
the tide travels at the average rate of 16 miles per hour, 
and it advances up Delaware Bay with about the same ve- 
locity. From Sandy Hook to New York city the tide ad- 
vances at the rate of 20 miles per hour, and it travels from 
New York to Albany at the average rate of nearly 16 miles 
per hour. 

256. Height of the Tides. — At small islands in mid-ocean 
the tides never rise to a great height — sometimes even less 
than one foot ; and the average height of the tides for the 
islands of the Atlantic and Pacific Oceans is only 3^- feet. 
Upon approaching an extensive coast, where the water is 
shallow, the velocity of the tidal wave is diminished, the co- 
tidal lines are crowded more closely together, and the height 
of the tide is thereby increased ; so that while in mid-ocean 
the average height of the tides does not exceed 3-J feet, the 
average in the neighborhood of continents is not less than 
4 or 5 feet. 



150 ASTRONOMY. 

257. Tides modified by the conformation of the Coast.— 
Along the coast of an extensive continent the height of 
the tides is greatly modified by the form of the shore line. 
When the coast is indented by broad bays which are open 
in the direction of the tidal wave, this wave, being contract- 
ed in breadth, increases in height, so that at the head of a 
bay the height of the tide may be twice as great as at the 
out ranee. Such a bay lies between Cape Florida and Cape 
Hatteras ; another lies between Cape Hatteras and Nan- 
tucket ; and another between Nantucket and Cape Sable. 
In the bay first mentioned, the range of the tides increases 
from two feet at the Capes to seven feet at Savannah. In 
the second bay, the range increases from two feet to nearly 
five feet at Sandy Hook ; and in the third bay, the tide in- 
creases from two feet at Nantucket to ten feet at Boston, 
and 18 feet at the entrance to the Bay of Fundy; while at 
the head of the bay it sometimes rises to the height of 70 
feet. This increase of height results from the contraction 
in the width of the channel into which the advancing wave 
is forced. 



Mmtucket C. 8 a blc 

258. Tides of Rivers, — The tides of rivers exhibit the 
operation of similar principles. The velocity varies with 
the depth of water; and the height of the tide increases 
where the river contracts, and decreases where the channel 

expands Hence, in ascending a long river, it may happen 

that the height of the tides may alternately increase and 

decrease Thus, at New York, the mean height of the tide 

is 4,8 feet; at West Point, fu) miles up the Hudson River, 

the tide rises only 2.7 feet; at Tivoli, 98 miles from New 



THE ti i) i 16] 

York, the tide rises 1 feet ; while at Albany it- rises only 

2.8 feet. 

259. Tidal Currents, The currents produced by the tides 
in the shallow waters of bays and rivers must not be eon- 
founded with the movement of the tidal wave. Their ve- 
locity is much less than that of the tidal wave, and the 
change of the current does no1 generally correspond in time 
to the change of the tide. The maximum current in Long 
bland Sound is about two miles per hour, and in New Fork 
Bay three miles per hour. In New York Bay the ebb stream 
begins at one sixth of the eh!> tide, while at Mont.'iuh Point 
the ei>l> stream does not, begin until half ebb tide. 

Tidal currents owe their origin partly to differences of 
level, and partly to the resistance opposed to the tidal wave 
by contracted channels and shallow water. Their velocity 
is greatest in narrow channels like Hell Gate and the Race 

oil' Fisher's Sound. 

260. Diurnal Inequality in the Weight oftlu Tides, On 
the Pacific coast of the United States, when the moon is far 
from the equator, there is one Large mid our; small tide dur- 
ing each day. At San Francisco the difference between high 

mid low water in the forenoon is sometimes only tWO inches, 

while in the afternoon of the same day the, difference is 5<£ 
feet. When the moon is on the equator, the two daily tides 

are nearly equal. 

At other places on the Pacific coast this inequality in the 
two daily tides is more, remarkable. Near Vancouver's M- 
and, in hit, 48°, when the moon has its greatest declination, 
there is no descent corresponding to morning low water, 
but merely a temporary check in the rise of' the tide. Thus 
one of the two daily tides becomes obliterated that is, we 
find hut one tide in 24 hours. Similar phenomena occur at 
places farther north along the Pacific coai t. 

Along the Atlantic coast of the United States, when the 
moon has its greatest declination, the difference between 

high water in the forenoon and afternoon averages ahout [8 

inches. On the coast of Europe the diurnal inequality is still 

-mailer, and at many places it can with difficulty he detected 



152 ASTItONOMI. 

261. Cause of these Variations in the Diurnal Inequality -. 
— The tide actually observed at any port is the effect, not 
simply of the immediate action of the sun and moon upon 
the waters of the ocean, but is rather the resultant of their 
continued action upon the waters of the different seas 
through which the wave has advanced from its first origin 
in the Pacific until it reaches the given port, embracing an 
interval sometimes of one or two days, and even longer. 
During this period the moon's action sometimes tends to 
produce a large tide and sometimes a small one ; and in a 
tide whose age is more than 12 hours, these different effects 
may be combined so as nearly to obliterate the diurnal ine- 
quality. This is probably the reason why the diurnal ine- 
quality is less noticeable in the North Atlantic than in the 
North Pacific. 

262. Tides of 'the Gulf of 'Mexico .—The Gulf of Mexico is 
a shallow sea, about 800 miles in diameter, almost entirely 
surrounded by land, and communicating with the Atlantic 
by two channels each about 100 miles in breadth. Since 
the width of the Gulf is so much greater than that of the 
channels through which the tidal wave enters, the height 
of the tide is very small. At Mobile and Pensacola the av- 
erage height is only one foot. The diurnal inequality is 
also quite large, so that at most places (except when the 
moon is near the equator) one of the daily tides is well-nigh 
inappreciable, and the tide is said to ebb and flow but once 
in 24 hours. 

263. Tides of Inland Seas. — In small lakes and seas which 
do not communicate with the ocean there is a daily tide, but 
so small that it requires the most accurate observations to 
detect it. There is a perceptible tide in Lake Michigan, the 
average height at Chicago being If inches. The ratio of 
this height to that of the tide in mid-ocean is about equal 
to the ratio of the length of the lake to the diameter of the 
earth. 

264. Tides of the Coast of Europe. — Along the coast of 
Europe the highest tides prevail in the Bristol Channel and 



THE TIDES. 153 

on the northwest coast of France. In the Bristol Channel 
the tides sometimes rise to the height of 70 feet, and at St. 
Malo to the height of 40 feet. The mean range of the spring 
tides at Liverpool is 26 feet, at London Docks about 20 feet, 
and at Portsmouth nearly 13 feet. These tides are not due 
to any peculiarity in the moon's immediate action at these 
localities, but are simply the mechanical effect of the tidal 
wave being forced up a narrow channel. 

The lowest tides occur on the eastern coast of Ireland, 
north of the entrance to St. George's Channel, where the 
range of the tides is only two feet. The tide is diverted 
from the coast of Ireland by a projecting promontory, and 
is driven upon the coast of Wales, where it rises to the 
height of 36 feet. 

265. The Establishment of a Port — The interval between 
the time of the moon's crossing the meridian and the time 
of high water at any port is nearly constant. The mean in- 
terval on the days of new and full moon is called the estab- 
lishment of the port. The mean interval at New York is 
8h. 13m. ; and the difference between the greatest and the 
least interval occurring in different parts of the month is 43 
minutes. 

The mean establishment of Boston is llh. 27m. ; of PhiLa« 
delphia,13h. 44m.; and of San Francisco, 12h. 6m. 

G2 



154 ASTRONOMY. 



CHAPTER XII. 

THE PLANETS — THEIR APPARENT MOTIONS. — ELEMENTS OF 
THEIR ORBITS. 

266. Number ', etc., of the Planets. — The planets are bod- 
ies of a globular form, which revolve around the sun as a 
common centre, in orbits which do not differ much from cir- 
cles. The name planet is derived from a Greek word signi- 
fying a wanderer, and was applied by the ancients to these 
bodies because their apparent movements were complicated 
and irregular. Five of the planets — Mercury, Venus, Mars, 
Jupiter, and Saturn — are very conspicuous, and have been 
known from time immemorial. Uranus was discovered in 
1781, and Neptune in 1846, making eight planets, including 
the earth. Besides these there is a large group of small 
planets, called asteroids, situated between the orbits of Mars 
and Jupiter. The first of these was discovered in 1801, and 
the number known at the end of 1868 was 107. 

The orbits of Mercury and Venus are included within the 
orbit of the earth, and they are hence called inferior plan- 
ets, while the others are called superior planets. The terms 
inferior and superior, as here used, do not refer to the mag- 
nitude of the planets, but simply to their position with re- 
spect to the earth and sun. 

267. The Orbits of the Planets. — The orbit of each of the 
planets is an ellipse, of which the sun occupies one of the 
foci. That point of the orbit of a planet which is nearest 
the sun is called the perihelion, and that point which is most 
remote from the sun is called the aphelion. 

The eccentricity of an elliptic orbit is the ratio which the 
distance from the centre of the ellipse to either focus bears 
to the semi-major axis. The eccentricities of most of the 
planetary orbits are so minute, that if the form of the orbit 
were exactly delineated on paper, it could not be distin- 
guished from a circle except by careful measurement. 



THE PLANETS. 155 

268. Geocentric and Heliocentric Places, etc. — The geocen- 
tric place of a body is its place as seen from the centre of 
the earth, and the heliocentric place is its place as it would 
be seen from the centre of the sun. 

A planet is said to be in conjunction with the sun when 
it has the same longitude, being then in nearly the same 
,?art of the heavens with the sun. It is said to be in op- 
position with the sun when its longitude differs by 180° 
from that of the sun, being then in the quarter of the 
heavens opposite to the sun. A planet is said to be in 
quadrature w T hen its longitude differs by 90° from that of 
the sun. 

An inferior planet is in conjunction with the sun when it 
is between the sun and the earth, as well as when it is on 
the opposite side of the sun. The former is called the infe- 
rior conjunction, the latter the superior conjunction. 

A planet, w T hen in conjunction with the sun, passes the 
meridian about noon, and is therefore above the horizon only 
during the day. A planet, when in opposition with the sun, 
passes the meridian about midnight, and is therefore above 
the horizon during the night. A planet, when in quadra- 
ture, passes the meridian about six o'clock either morning 
or evening. The angle formed by lines drawn from the 
earth to the sun and a planet is called the elongation of the 
planet from the sun, and it is east or west, according as the 
planet is on the east or west side of the sun. 

269. The Satellites. — Some of the planets are centres of 
secondary systems, consisting of smaller globes revolving 
around them in the same manner as they revolve around the 
sun. These secondary globes are called satellites or moons. 
The primary planets which are thus attended by satellites 
carry the satellites with them in their orbits around the sun. 
Of the satellites known at the present time, four revolve 
around Jupiter, eight around Saturn, four around Uranus, 
and one" around Neptune. The Moon is also a satellite to 
the earth. 

270. Why the apparent Motions of the Planets differ from 
the real Motions. — If the planets could be viewed from tha 



156 ASTRONOMY. 

sun as a centre, they would all be seen to advance invariably 
in the same direction, viz., from west to east, in planes only 
slightly inclined to each other, but with very unequal veloci- 
ties. Mercury would advance eastward with a velocity 
about one third as great as our moon; Venus would ad- 
vance in the same direction with a velocity less than halt 
that of Mercury ; the more distant planets would advance 
still more slowly ; while the motions of Uranus and Neptune 
would be scarcely appreciable except by comparing observa 
tions made at long intervals of time. None of the planets 
would ever appear to move from east to west. 

The motions of the planets as they actually appear to us 
are very unlike those just described : first, because we view 
them from a point remote from the centre of their orbits, so 
that their distances from the earth are subject to great va- 
riations ; and, second, because the earth itself is in motion, 
and hence the planets have an apparent motion resulting 
from the real motion of the earth. 

271. The apparent Motion of an Inferior Planet. — In or- 
der to deduce the apparent motion of an inferior planet from 
its real motion, let CKZ represent a portion of the heavens 
lying in the plane of the ecliptic; let a, 6, c f d, etc., be the 
orbit of the earth; and 1,2,3,4, etc., be the orbit of Mer- 
cury. Let the orbit of Mercury be divided into 12 equal 
parts, each of which is described in 7 \ days ; and let a£, be. 
cd, etc., be the spaces described by the earth in the same 
time. Suppose that when the earth is at the point a, Mer- 
cury is at the point 1 ; Mercury will then appear in the 
heavens at A, in the direction of the line a\. In 7 J days 
Mercury will have arrived at 2, while the earth has arrived 
at 5, and therefore Mercury will appear at B. When the 
earth is at c, Mercury will appear at C, and so on. By laying 
the edge of a ruler on the points c and 3, d and 4, e and 5, 
and so on, the successive apparent places of Mercury in the 
heavens may be determined. We thus find that from A to 
C his apparent motion is from east to west ; from C to P his 
apparent motion is from west to east ; from P to T it is from 
east to west ; and from T to Z the apparent motion is from 
west to east, 



Pig. 83. 



THE PLANETS. 



155 




272. Direct and Retrograde Motion. — When a planet ap- 
pears to move among the stars in the direction in which the 
sun appears to move along the ecliptic, its apparent motion 
is said to be direct ; and when it appears to move in the 
contrary direction, its motion is said to be retrograde. The 
apparent motion of the inferior planets is always direct, ex- 
cept near the inferior conjunction, when the motion is retro- 
grade. 

If we follow the movements of Mercury during several 
successive revolutions, we shall find its apparent motion to 
be such as is indicated by the arrows in Fig. 83. Xear in- 
ferior conjunction its motion is retrograde from A to C. As 
it approaches C, its apparent motion westward becomes 
gradually slower until it stops altogether at C, and becomes 
stationary. It then moves eastward until it arrives at P, 
where it again becomes stationary, after which it again 
moves westward through the arc PT, when it again be- 



158 



ASTRONOMY. 



comes stationary, and so on. The middle point of the arc 
of progression, CP, is that at which the planet is in superior 
conjunction ; and the middle point of the arc of retrogres- 
sion, PT, is that at which the planet is in inferior conjunc- 
tion. 

These apparently irregular movements suggested to the 
ancients the name of planet, or wanderer. 

Fig. 84 shows the apparent motion of Venus for a period 
of five months. 



Fig. 84. 





Fdi.11 


March 1. 








"»»-*■ 


lTarU&w 


itr— ~~ZZ^^ 


AprdL^ 




ECLIPTIC 










****'). 1810 ~— 






-< =a ilwas, 


1Se9Dec£ 



io°X 



5°jr. 



jssr. 



273. Apparent Motion of a Superior Planet. — In order to 
deduce the apparent motion of a superior planet from the 
real motions of the earth and planet, let S be the place of 
the sun ; 1, 2, 3, etc., be the orbit of the earth ; a, #, c, etc., 
the orbit of Mars ; and CGL a part of the starry firmament. 
Let the orbit of the earth be divided into 12 equal parts, 
each of which is described in one month ; and let ab, be, cd, 
etc., be the spaces described by Mars in the same time. 
Suppose the earth to be at the point 1 when Mars is at the 
point a, Mars will then appear in the heavens in the direc- 
tion of the line la. When the earth is at 3 and Mars at 
c, he will appear in the heavens at C. While the earth 
moves from 4 to 5, and from 5 to 6, Mars will appear to 
have advanced among the stars from D to E, and from E to 
F, in the direction from east to west. During the motion 
of the earth from 6 to 7, and from 7 to 8, Mars will appear 
to go backward from F to G, and from G to H, in the direc- 
tion from east to west. During the motion of the earth 
from 8 to 9, and from 9 to 10, Mars will appear to advance 
from H to I, and from I to K, in the direction from west to 
east, and the motion will continue in the same direction un- 
til near the succeeding opposition. 

The apparent motion of a superior planet projected on 



THE PLANETS. 



159 



Pig. 85 





the heavens is thus seen to be similar to that of an inferior 
planet, except that the retrogression of the inferior planets 
takes place near inferior conjunction, and that of the supe- 
rior planets takes place near opposition. 

Fig. 86 shows the apparent motion of Mars during a pe- 
riod of nine months. 

Fig. 86. 




ISC" ECLIPTIC. M° 



274. Conditions under which a Planet is Visible. — One or 
two of the planets are sometimes seen when the sun is above 
the horizon ; but generally, in order to be visible without a 
telescope, a planet must have an elongation from the sun of 
at least 30°, so as to be above the horizon after the close of 
the evening twilight, or before the commencement of the 
morning twilight. 



160 ASTRONOMY. 

The greatest elongation of the inferior planets never ex- 
ceeds 47°. If they are east of the sun, they pass the merid- 
ian in the afternoon, and being visible above the horizon 
after sunset, are called evening stars. If they are west of 
the sun, they pass the meridian in the forenoon, and being 
visible above the eastern horizon before sunrise, are called 
morning stars. 

A superior planet, having any degree of elongation from 
0° to 180°, may pass the meridian at any hour of the day or 
night. At opposition, the planet passes the meridian at mid- 
night, and is therefore visible from sunset to sunrise. 

275. Phases of the Planets. — The inferior planets exhibit 
the same variety of phases as the moon. At the inferior 
conjunction the dark side of the planet is turned directly to* 
ward the earth. Soon afterward the planet appears a thin 
crescent, which increases in breadth until at the greatest 
elongation it becomes a half moon. After this the planet 
becomes gibbous, and at superior conjunction it appears a 
full circle. These phases are easily accounted for by suppos- 
ing the planet to be an opaque spherical body, which shines 
by reflecting the sun's light. 

The distances of the superior planets from the sun are 
(with the exception of Mars) so much greater than that of 
the earth, that the hemisphere which is turned toward the 
earth is sensibly the same as that turned toward the sun, 
and these planets always appear full. 

276, Distinctive Peculiarities of Different Planets. — The 
planets can generally be distinguished from each other ei- 
ther by a difference of aspect or by a difference of their ap- 
parent motions. The two most brilliant planets are Venus 
and Jupiter. They are similar in appearance, but their ap- 
parent motions among the stars are very different. Thus 
Venus never recedes beyond 47° from the sun, while Jupiter 
may have any elongation up to 180°. Mars may be distin- 
guished by his red or fiery color, while Saturn shines with 
a faint reddish light. 



*&* 



277. Elements of the Orbit of a Planet. — In order to be 



THE PLANETS, 16 1 

able to compute the place of a planet for any assumed time, 
it is necessary to know for each planet the position and di- 
mensions of its orbit, its mean motion, and its place at a 
specified epoch. The quantities necessary to be known for 
this computation are called the elements of the orbit , and are 
seven in number, viz. : 

1 The periodic time. 

2 The mean distance from the sun, or the semi-major axis 
cf the orbit. 

3. The longitude of the ascending node. 

4. The inclination of the plane of the orbit to the plane of 
the ecliptic. 

5. The eccentricity of the orbit. 

6. The heliocentric longitude of the perihelion. 

7. The place of the planet in its orbit at some specified 
epoch. 

The third and fourth elements define the position of the 
plane of the planet's orbit ; the second and fifth define the 
form and dimensions of the orbit ; and the sixth defines the 
position of the orbit in its plane. 

If the mass of a planet is known, or is so small that it may 
be neglected, the mean distance can be computed from the 
periodic time by means of Kepler's third law, in which case 
the number of elements will be reduced to six. 

The orbits of the planets can not be determined in the 
same manner as that of the moon, Art. 185, because the cen- 
tre of the earth may be regarded as a fixed point relative to 
the moon's orbit, but it is not fixed relative to the planetary 
orbits. The methods therefore employed for determining 
the orbits of the planets are in many respects quite differ- 
ent from those which are applicable to determining the or- 
bit of the moon, and also that of the earth. 

278. To find the Periodic Time, — Each of the planets, 
during about half its revolution around the sun, is found to 
be on one side of the ecliptic, and during the other half on 
the opposite side. The interval which elapses from the 
time when a planet is at one of its nodes till its return to 
the same node (allowance being made for the motion of the 
nodes), is the sidereal period of the planet. When a planet 



162 ASTRONOMY. 

is at either of its nodes it is in the plane of the ecliptic, and 
its latitude is then zero Let the right ascension and dec- 
lination of a planet be observed from day to day near the 
period when it is passing a node, and let these places be con- 
verted into longitudes and latitudes From these we may, 
by a proportion, obtain the time when the planet's latitude 
was zero. If similar observations are made when the plan- 
et passes the same node again, w r e shall have the time of a 
revolution. 

When the orbit of a planet is but slightly inclined to the 
ecliptic, a small error in the observations has a great influ- 
ence on the computed time of crossing the ecliptic. A more 
accurate result will be obtained by employing observations 
separated by a long interval, and dividing this interval by 
the number of revolutions of the planet, 

279. Sidereal Period deduced from the Sy?iodic« — The sy- 
nodical period of a planet is the interval between two con- 
secutive oppositions, or two conjunctions of the same kind. 
If we compare the instant of an opposition which has been 
observed in modern times w T ith that of an opposition ob- 
served by the earlier astronomers, and divide the interval 
between them by the number of synodic revolutions con- 
tained in it, w r e may obtain the mean synodical period very 
accurately. From the synodical period, the sidereal period 
may be deduced by computation. 

280. To find the Distance of a Planet from the Sun. — 
Fig. 97. The distance of an inferior planet from the 

sun may be determined by observing the an- 
gle of greatest elongation. 

In the triangle SEV, let S be the place of 
the sun,E the earth, and V an inferior planet at 
the time of its greatest elongation. Then, 
since the angle SVE is a right angle, we have 

SV:SE:: sin. SEV: radius; 
or SV = SEsin.SEV. 

If the orbits of the planets were exact cir- 
E cles, this method would give the mean distance 

of the planet from the sun ; but since the orbits are ellip- 




THE PLANETS. 



1G3 



tical, we must observe the greatest elongation in different 
parts of the orbit, and thus obtain its average value, whence 
its mean distance can be computed. 

The distance of a superior planet whose periodic time is 
known may be found by measuring the retrograde motion 
of the planet in one day at the time of opposition. 

28L Diameters of the Planets, — Having determined the 
distances of the planets, it is only necessary to measure their 
apparent diameters, and we can easily compute their abso- 
lute diameters in miles. The apparent diameters of the plan- 
ets are variable, since they depend upon the distances, which 
are continually varying. In computing the absolute diam- 
eter of a planet we must therefore combine the apparent di- 
ameter with the distance of the planet at the time of obser- 
vation. 



282. The mean distances of the planets from the sun, ex- 
pressed in miles, are in round numbers as follows : Mer- 
cury, 35 millions ; Venus, 66 millions ; the Earth, 92 millions ; 
Mar?, 140 millions ; Asteroids, 245 millions ; Jupiter, 478 mil- 
lions; Saturn, 876 millions; Uranus, 1762 millions; and Nep- 
tune, 2758 millions. The distance of Neptune is 77 times 
that of Mercury, and 30 times that of the earth. 

Fig. 88. 



SATURN & SA TELUTES. 




164 ASTRONOMY. 

Fig. 88 shows the relative distances of the planets from 
the sun, with the exception of the two most distant ones, 
which are shown on Fig. 101, page 187. 

The approximate periods of revolution of the planets are: 
of Mercury, 3 months ; Venus, 7-^ months ; the Earth, 1 year; 
Mars, 2 years; Asteroids, 4-^ years; Jupiter, 12 years; Sat- 
urn, 29 years ; Uranus, 84 years; and Neptune, 164 years. 
The periods and mean distances are more exactly given in 
Tables I. and II., pages 247 and 248. 

283. Hoio to determine the Mass and Density of a Planet. 
— The quantity of matter in those planets which have satel- 
lites may be determined by comparing the attraction of the 
planet for one of its satellites w T ith the attraction of the sun 
for the planet. These forces are to each other directly as 
the masses of the planet and the sun, and inversely as the 
squares of the distances of the satellite from the planet, and 
of the planet from the sun. 

The quantity of matter in those planets which have no 
satellites may be determined from the perturbations which 
they produce in the motions of other planets, or one of the 
periodic comets. 

Having determined the quantity of matter in the sun and 
planets, and knowing also their volumes, Art. 281, we can 
compute their densities, for the densities of bodies are pro- 
portional to their quantities of matter divided by their vol* 
ume. Knowing also the specific gravity of the earth, Art. 
45, we can compute the specific gravity of each member of 
the solar system. 



BLEJ2CU&Y AND VEXUS. 



165 



chapter xnr. 

THE INTERIOR PLANETS, MERCURY AND YENCS. - — TRANSITS. 

284. Greatest Elongations of Mercury and Venus, — Since 
the orbits of Mercury and Venus are included within that 
of the Earth, their elongation or angular distance from the 
sun is never great. They appear to accompany the sun, be- 
ing seen alternately on the east and west side of it. 

Let S be the place of the sun, E that of the earth, MA the 
orbit of Mercury, and M the place of the Fi<?.S9. 

planet when at its greatest elongation, at 
which time the angle EMS is a right angle. 
Since the distances of the sun from the earth 
and planet are variable, the greatest elonga- 
tion of the planet is variable. The elongation 
will be the greatest possible when SE is least 
and SM is greatest ; that is, when the earth 
is in perihelion and Mercury in aphelion, at 
which time the greatest elongation of Mer- 
cury is 28° 20'; but when the earth is in 
aphelion and Mercury in perihelion, the greatest elongation 
is only 17° 36'. 

In a similar manner we find the greatest elongation of 
Venus to vary from 45° to 47° 12'. 




285. Phases of Mercury and Venus. — To the naked eye 
the discs of all the planets appear circular, but when ob- 
served with a telescope the planets Mercury and Venus ex- 
hibit the same variety of phases as the moon. Xear supe- 
rior conjunction at A, the planet is lost for a little time in 
the sun's rays ; when first seen after sunset its disc is nearly 
circular, but it soon becomes gibbous, and at the greatest 
elongation at B we see only half the disc illuminated. As 
the planet advances toward inferior conjunction, the form 
becomes that of a crescent, with the horns turned from the 
Bun 3 until it is again lost in the sun's rays at C. In passing 



266 



ASTRONOMY. 



Fig, 00. 




O— 9 




#-•-• 



from inferior to superior conjunction, the same variety of 
phases is exhibited, but in the inverse order. 

These phases are accounted for by supposing the planet 
to be an opaque spherical body which shines by reflecting 
the sun's liirlit. 

o 

MERCURY, 

286. Period, Distance from the Sk?k etc. — Mercury per- 
forms its revolution around the sun in a little less than three 
months, but its synodic period, or the time from one inferior 
conjunction to another, is L16 days, or nearly four months. 

Its mean distance from the sun is 35 millions o( miles. 
The eccentricity of its orbit is oneJifth,&0 that its distance 
from the sun, when at aphelion, is 42 millions of miles, but 
at perihelion it is only 28 millions. 

When between the earth and the sun, the disc of Mercury 
subtends an angle of about 12 seconds, but near the superioi 
conjunction it subtends an angle of only 5 seconds. Its real 
diameter is about 8000 miles. 

287, Visibility of Mercury. — Since the elongation of Mer- 
cury from the sun never exceeds 28°, this planet is seldom 
Been except in strong twilight either morning or evening, 
but it often appears as conspicuous as a star o{ % the first 
magnitude would be in the same part of the heavens. The 
circumstances favorable to its visibility are, first, a clear at- 
mosphere; second, a short twilight; third, the planet should 
bo near aphelion; and, fourth, the planet should be on the 
north side oi' the ecliptic. 



VENUS. 167 

288. Time of greatest Brightness. — Mercury docs not ap- 
pear most brilliant when its disc is circular like a full moon, 
because its distance from us is then too great ; neither when 
it is nearest to us, because then almost the entire illumined 
part is turned away from the earth. The greatest bright- 
ness must then occur at some intermediate point. This point 
is near the greatest elongation. When Mercury is an even- 
ing star, the greatest brightness occurs a few days before 
the greatest elongation ; when it is a morning star, the 
greatest brightness occurs a few days after the greatest 
elongation. 

289. Rotation on its Axis. — By observing Mercury with 
powerful telescopes, some astronomers have supposed that 
they discovered distinct spots upon it, and by observing 
these from day to day, it has been concluded that the plan- 
et performs a rotation on its axis in 24h. 5^m. Other astron- 
omers, w^ith equally good means of observation, have never 
remarked upon the planet's surface any spots by which they 
could approximate to the time of rotation. 

There is but little difference between the polar and equa- 
torial diameters of the planet, and the compression does not 
probably exceed y^. 

VENUS. 

290. Period, Distance, and Diameter. — Venus is the most 
brilliant of all the planets, and is generally called the even- 
ing or the morning star. It revolves round the sun in about 
Y-g- months, but its synodic period, or the time from one in- 
ferior conjunction to the next, is about 19 months. Its mean 
distance from the sun is 6Q millions of miles ; and, since the 
eccentricity of its orbit is very small, this distance is subject 
to but slight variation. 

The apparent diameter of Venus varies more sensibly than 
that of Mercury, owing to the greater variation of its dis- 
tance from the earth. At inferior conjunction it subtends 
an angle of 64 seconds, while at superior conjunction its di- 
ameter is less than 10 seconds. Its real diameter is 7800 
miles, or nearly the same as that of the earth. 



1G8 



ASTRONOMY. 



291, Venus visible in the daytime* — The greatest elon- 
gation of Venus from the sun amounts to 47°, and, on ac- 
count of its proximity to the earth, it is one of the most 
beautiful objects in the firmament. When it rises before 
the sun it is called the morning star; when it sets after the 
sun, it is called the evening star. When most brilliant, it 
can be distinctly seen at midday by the naked eye, especial- 
ly if it is also near its greatest north latitude. Its bright- 
ness is greatest about :*C days before and after inferior con- 
junction, when its elongation is about 40°, and the enlight- 
ened part of the disc not more than one quarter of a circle. 
At these periods the light is so great that it casts a sensible 
shadow at night. 



292. Rotation on an Axis. Twilight. — Astronomers have 
frequently seen upon Venus irregularities, or dusky spots, 
and have found that these appearances recurred at equal 
intervals of about 23^ hours ; whence it is inferred that this 
is the time of one rotation of the planet. 

The edge of the enlightened part of the planet — that is, 
the boundary of the illuminated and dark hemispheres — 
Fi£. oi. is shaded, or the light gradually 

fades away into the darkness. This 
phenomenon is analogous to twi- 
light upon the earth, and indicates 
the existence of a dense atmosphere. 
Moreover, when the disc is seen as 
a narrow crescent, a faint light 
stretches from the horns of the cres- 
cent beyond a semicircle ; and when 
very near conjunction, an entire ring 
o!l light has sometimes been seen 
surrounding the planet. This ap- 
pearance is due to the refraction of the sun's rays by the at- 
mosphere of the planet, and it has been computed that the 
atmosphere of Venus is one fourth denser than that of the 
earth. 




TRANSITS OF MERCURY AND VENUS. 169 



TRANSITS OF MERCURY AND VENUS. 

293. Mercury and Venus sometimes pass between the sun 
and earth, and are seen as black spots crossing the sun's 
disc. This phenomenon is called a transit of the planet. It 
takes place whenever, at the time of inferior conjunction, 
the planet is so near its node that its distance from the eclip 
tic is less than the apparent semi-diameter of the sun. 

294. When Transits are possible. — Transits can only take 
place when the planet is within a small distance of its node. 
Let X represent the node of the Fig. 92. p 

planet's orbit ; S the centre of N~— ==Z T ' /TV 
the sun's disc on the ecliptic, \J*S 

and at such a distance from the node that the edge of the 
disc just touches the orbit NP of the planet. A transit is 
possible only when the distance of the sun's centre from the 
node is less than NS. 

Transits can therefore only happen when the earth is near 
one of the nodes of the planet's orbit. Those of Mercury 
must occur either in May or November, while those of Venus 
occur either in June or December. The last transit of Mer- 
cury occurred November 4, 1868, and the next will occur 
May 6,1878. The last transit of Venus occurred June 3, 
1769, and the next will occur December 8, 1874. 

295. Sun's Parallax and Distance. — The transits of Ve- 
nus are important, since they furnish a method by which the 
sun's distance from the earth can be determined with great- 
er precision than by any other known method. The tran- 
sits of Mercury afford a similar method, but less reliable, on 
account of the greater distance of that planet from the earth. 

At the time of a transit, observers at different stations 
upon the earth refer the planet to different points upon the 
sun's disc, so that the transit takes place along different 
chords, and is accomplished in unequal periods of time. Let 
the circle FHKG represent the sun's disc ; let E represent 
the earth, and A and B the places of two observers, sup- 
posed to be situated at the opposite extremities of that di- 
ameter of the earth which is perpendicular to the ecliptic; 

H 



L70 



ASTRONOMY. 

Fig. 93. 




also let V be Venus moving in the direction represented by 
the arrow. To the observer at A the planet will appear to 
describe the chord FG, and to the observer at B the paral- 
lel chord HK. Also, when to the observer at A the centre 
of the planet appears to be at D, to the observer at B it will 
appear to be at C. 

Now, by similar triangles, we have 

AV:DV::AB:CD. 
The relative distances of the planets from the sun can be 
computed by Kepler's third law when we know their pe- 
riods of revolution. Hence we can compute the value of 
CD expressed in miles. 

The value of CD expressed in seconds may be derived 
from the observed times of beginning and ending of the 
transit at A and B. Each observer notes the time when 
the disc of the planet appears to touch the sun's disc on the 
Fig. 94. outside at L, and also on the inside at M, 

and again when the planet is leaving the 
sun's disc. Then, since the planet's rate 
of motion is already known, the number 
of seconds in the chord described by the 
planet can be computed. Knowing the 
length of DG, which is the half of FG, 
and knowing also SG, the apparent radius of the sun, we 
can compute SD. In the same manner, from the length of 
the chord HK, we can compute SC. The difference between 
these lines is the value of CD, supposed to be expressed in 
seconds. But we have already ascertained the value of CD 
in miles ; hence we can determine the linear value of one 
second at the sun as seen from the earth, which is found to 
be 462 miles; and hence the angle which the earth's radius 
subtends at the sun will be 4nnr, or 8".58. This angle is 
called the sun's horizontal parallax ; and from it, when we 




TRANSIT OF VENUS. 1 71 

know the radius of the earth, we can compute the distance 
of the earth from the sun. 

296. Observations of Transit of 1769. — Expeditions were 
fitted out by several of the governments of Europe, and sent 
to remote parts of the earth, to observe the transit of Venus 
in 1769. The value of the sun's parallax deduced by Pro- 
fessor Encke from these observations is 8 ".5 8, but recent 
computers have deduced from the same observations the 
value 8". 91. 

As there is some uncertainty respecting the exact value 
of the sun's parallax, and consequently an uncertainty re- 
specting the distance of the earth from the sun, astronomers 
are accustomed to call the mean distance of the earth from 
the sun unity, and estimate all distances in our planetary 
system by reference to this unit. 



jf2 ASTRONOMY. 



CHAPTER XIV. 

THE SUPERIOR PLANETS — THEIR SATELLITES. 

297. How the Superior Planets are distinguished from the 
Inferior, — Since the superior planets revolve in orbits ex- 
terior to that of the earth, they never come between us and 
the sun — that is, they have no inferior conjunction; but 
they are seen in superior conjunction and in opposition ; not 
do they exhibit to us phases like those of Mercury and Ve- 
nus. The disc of Mars sometimes appears gibbous ; but the 
other superior planets are so distant that their enlightened 
surface is always turned nearly toward the earth, and the 
gibbous form is not perceptible. 

MARS. 

298. Period, Distance, etc. — Mars makes one revolution 
about the sun in 23 months ; but its synodic period, or the 
interval from opposition to opposition, is 26 months. 

Its mean distance from the sun is 140 millions of miles ; 
but, on account of the eccentricity of its orbit, this distance 
is subject to a variation of nearly one tenth its entire amount. 
Its greatest distance from the sun is 152 millions of miles, 
and its least distance 127 millions. 

The distance of Mars from the earth at opposition is some- 
times only 34 millions of miles, while at conjunction it is 
sometimes as great as 245 millions. Its apparent diameter 
varies in the same ratio, or from 3" to 24". Its real diam- 
eter is 4500 miles. 

299. Phases, Potation, etc. — At conjunction and opposi- 
tion, since the same hemisphere is turned toward the earth 
and sun, the planet appears circular, as shown at M, and M 5 . 
Id all other positions it appears slightly gibbous; but the 
deficient portion never exceeds about one ninth of a hemi' 
sphere. 



THE SUPERIOR PLANETS. 



173 



Big. £5. ^^-O — - -^ When examined with 

a good telescope, the 
surface of Mars is seen 
to be diversified with 
large spots of different- 
shades, which, with oc- 
casional variations, re- 
tain always the same 
size and form. These 
are supposed to be con- 
tinents and seas ; and 
by observing these 
spots, the planet has 
been found to make one 
rotation upon its axis in 24^ hours, and its axis is inclined 
to the plane of its orbit about 60°. 

Hence we see that on Mars the days and nights are nearly 
of the same length as on the earth ; and the year is diversi- 
fied by a change of seasons, not very different from what 
prevails on our own globe. 




300. Spheroidal Form. — The polar diameter of Mars is 
sensibly less than the equatorial, the difference according to 
some measurements amounting to one fiftieth, and accord- 
ing to others to one thirty-ninth of the equatorial diameter. 



Fig. 96. 



301. Telescopic Appearance. — Many of the spots on this 
planet retain the same forms, with the same varieties of light 
and shade, even at the most distant intervals of time. But 
about the polar regions are some- 
times seen white spots, with a well- 
defined outline, which are conject- 
ured to be s?iow, since they are re- 
duced in size and sometimes disap- 
pear during their protracted sum- 
mer, and are greatest when first 
emerging from the long night of 
their polar winter. 

Mars usually shines with a red or 
fiery light ; but this redness is more 




174 ASTRONOMY. 

noticeable to the naked eye than when viewed with a tel* 
escope. This color is probably the result of the tinge of the 
general soil of the planet. 

302. Sun's Parallax. — When Mars is in opposition, it 
sometimes approaches almost as near to the earth as Venus 
does at inferior conjunction. Its horizontal parallax then 
amounts to 22". From the parallax of Mars the parallax of 
the sun is easily computed, since the relative distances of 
the Earth and Mars from the sun may be determined from 
the times of revolution. The horizontal parallax of the sun 
which has been deduced from these observations is 8". 95. 
The mean of the best results which have been obtained for 
the sun's parallax is 8". 9, which is probably correct to with- 
in a small fraction of a second. 

THE MINOR PLANETS, OR ASTEROIDS. 

303. A deficient Planet beticeen Mars and Jupiter. — It 
was long ago discovered that there w r as something like a 
regular progression in the distances of the planets from the 
sun, and it was perceived that these distances conformed to 
a tolerably simple law, if we supplied an intermediate term 
between Mars and Jupiter. It was hence suspected that in 
this part of the solar system there existed a planet hitherto 
undiscovered; and in 1800 there was formed an association 
of observers for the purpose of searching for the supposed 
planet. 

In 1801, Piazzi, an Italian astronomer, discovered the plan- 
et Ceres, and its distance corresponded very nearly with 
that required by the law just referred to. 

In 1802, Dr. Olbers, while searching for Ceres, discovered 
another planet whose orbit had nearly the same dimensions 
as that of Ceres. This planet was called Pallas. 

304. Hypothesis of Olbers. — The minuteness of these two 
bodies, and their near approach to each other, led Olbers to 
suppose that they were the fragments of a much larger 
planet once revolving between Mars and Jupiter, and which 
had been broken into pieces by volcanic action or by some 
internal force. He concluded that other fragments prob* 



THE MINOR PLANETS. 175 

ably existed, and immediately commenced a search for 
them. 

In 1804, Harding discovered a third planet, whose mean 
distance from the sun was nearly the same as that of Ceres 
and Pallas. This planet was named Juno. 

In 1 807, Olbers discovered a fourth planet, whose orbit had 
nearly the same dimensions as those of the preceding. This 
planet was named Vesta. 

305. Number of the Asteroids. — Olbers continued his 
search for planets till 1816 without farther success. In 
1845, Hencke, a Prussian observer, after many years' search, 
discovered another small planet, which has been named As- 
traea. Since that time the progress of discovery has been 
astonishingly rapid, the total number of asteroids known in 
1868 amounting to 107. 

On account of the close resemblance in appearance be- 
tween these small planets and the fixed stars, Herschel pro- 
posed to call them Asteroids. Some astronomers employ 
the term Planetoid ; but the term minor planet is more de- 
scriptive, and is now in common use among astronomers. 

306. Brightness of the Asteroids. — The asteroids are all 
extremely minute, the largest of them being estimated at 
228 miles in diameter. Vesta is the only one among them 
which is ever visible to the naked eye, and this only under 
the most favorable circumstances. They all closely resem- 
ble small stars, and are only to be distinguished from fixed 
stars by their motion. Many of them are so small that they 
can be seen only near the opposition, even by the largest 
telescopes. 

It is probable that there is a multitude of asteroids yet 
remaining to be discovered. 

307. Distance of the Asteroids. — The average distance 
from the sun of the asteroids hitherto discovered is 2.67, or 
245 millions of miles; but their distances differ widely from 
each other. The asteroid nearest to the sun is Flora, with 
a mean distance of 200 millions of miles; the asteroid most 
remote from the sun is Sylvia, with a mean distance of 320 



178 ASTRONOMY. 

millions of miles. The orbit of Flora is therefore nearer to 
that of Mars than to that of Sylvia. 

308. Is Others' s hypothesis admissible? — The hypothesis 
of Olbers has lost most of its plausibility since the discovery 
of so many asteroids. If these bodies had once composed a 
single planet which burst into fragments, then, since the 
fragments all started from a common point, each must return 
to the same point in every revolution ; that is, all the orbits 
should have a common point of intersection. Such, however, 
is far from being the case. The orbits are spread over a large 
extent, and the smallest of the orbits is every where distant 
from the largest by at least 50 millions of miles. 

JUPITER. 

309. Period, Distance, etc. — Jupiter makes one revolution 
about the sun in 12 years, but the interval between two suc- 
cessive oppositions is 399 days. 

Its mean distance from the sun is 478 millions of miles; 
and, since the eccentricity of its orbit is about -^th, this dis- 
tance is augmented in aphelion and diminished in perihelion 
by 24 millions of miles. On account of its great distance 
from the sun, Jupiter exhibits no sensible phases. 

Jupiter is the largest of the planets, its volume exceeding 
the sum of all the others. Its equatorial diameter is 88,000 
miles, or 11 times that of the Earth, and its volume is 1300 
times that of the Earth. When near opposition, Jupiter is 
more conspicuous than any other planet except Venus, and 
is easily seen in the presence of a strong twilight. 

310. Rotation on an Axis, etc. — Permanent marks have 
been occasionally seen on Jupiter's disc, by means of which 
its rotation has been distinctly proved. The time of one ro- 
tation is 9h 56m. A particle at the equator of Jupiter must 
therefore move with a velocity of more than 450 miles per 
minute, or 27 times as fast as a place on the terrestrial 
equator. 

Jupiter's equator is but slightly inclined to the plane of 
its orbit, and hence the change of temperature with the sea- 
sons is very small. 



JUPITER. 177 

The disc of Jupiter is not circular, the polar diameter be- 
ing to the equatorial as 16 to 17. This oblateness is found 
by computation to be the same as would be produced upon 
a liquid globe making one rotation in about ten hours. 

311. Belts of Jupiter. — When examined with a good tel- 
escope, Jupiter's disc exhibits a light yellowish color, and 
has several brownish -gray streaks, called belts, which are 




nearly parallel to the equator of the planet. Two belts are 
generally most conspicuous, one north and the other south 
of the equator, separated by a light zone. Near the poles 
the streaks are more faint and less regular. These belts, al- 
though tolerably permanent, are subject to slow variations, 
such that, after the lapse of some months, the appearance of 
the disc is totally changed. Occasionally spots are seen 
upon the belts so well defined as to afford the means of de- 
termining the time of the planet's rotation. 

312. Cause of the Belts. — It is inferred that Jupiter is sur- 
rounded by an atmosphere, in which float dense masses of 
clouds, which conceal a considerable portion of the surface 
of the planet. The brightest portion of the disc probably 
consists of dense clouds which reflect the light of the sun, 
while the dusky bands are portions of the atmosphere near- 
ly free from clouds, and showing the surface of the planet 
with more or less distinctness. 

The arrangement of the clouds in lines parallel to the 
equator is probably due to atmospheric currents analogous 
to our trade winds, but more steady and decided, on ac- 

112 



178 ASTRONOMY. 

count of the more rapid rotation and greater diameter of 
Jupiter. 

313. Jupiter* s Satellites. — Jupiter is attended by four 
moons, or satellites, revolving round the primary, as our 
moon revolves around the Earth, but with a much more 
rapid motion. They are numbered first, second, etc., in the 
order of their distances from the primary. They were dis- 
covered by Galileo in 1610, soon after the invention of the 
telescope. 

The nearest moon completes a revolution in 42 hours, in 
an orbit whose radius is 270,000 miles. The second satel- 
lite completes a revolution in 85 hours, at a distance of 
420,000 miles. The third satellite completes a revolution 
in 172 hours, at a distance of 675,000 miles. The fourth 
satellite completes a revolution in 400 hours, at a distance 
of 1,200,000 miles. 

The diameter of the smallest satellite is 2200 miles, being 
the same as the diameter of our moon, and the diameter of 
the largest satellite is 3500 miles. The satellites shine with 
the brilliancy of stars of between the sixth and seventh mag- 
nitude ; but, on account of their proximity to the planet, 
which overpowers their light, they are generally invisible 
without the aid of a telescope. They move alternately from 
one side of the planet to the other nearly in a straight line. 
Sometimes all are on the right of the planet, and sometimes 
all are on the left of it, but generally we find one or two on 
each side. 

314. Eclipses of the Satellites, etc. — Jupiter's satellites fre- 
quently pass into the shadow of the primary and become in- 
visible. The length of Jupiter's shadow is more than 50 
millions of miles ; and, since the distance of the most remote 
satellite is but little over one million miles, if the orbits of 
the satellites lay in the plane of Jupiter's orbit, an eclipse 
of each satellite would occur at every revolution. In fact, 
the orbits of the satellites are inclined about three degrees 
to the plane of Jupiter's orbit, so that the fourth satellite 
sometimes passes through opposition without entering the 
shadow. 




Let JJ' represent the planet Jupiter; JVJ', its conical 
shadow; SS', the sun; E and E", the positions of the Earth 
when the planet is in quadrature ; and let ADFK represent 
the orbit of one of the satellites whose plane we will sup- 
pose to coincide with the ecliptic. From E draw the lines 
EJ, EJ', meeting the path of the satellite at H and K, as 
also at C and D. Let A and B be the points where the path 
of the satellite crosses the limits of the shadow. 

In the revolution of the satellites about the planet, four 
different classes of phenomena are observed: 

1st. When a satellite passes into the shadow of the plan- 
et, it is said to be eclipsed. The satellite disappears at A 
and reappears at B. 

2d. When a satellite, passing behind the planet, is between 
the lines EJC and EJ'D, it is concealed from our view by 
the interposition of the body of the planet. This phenom- 
enon is called an occultation of the satellite by the planet. 
The satellite disappears at C and reappears at D. 

3d. When a satellite passes between the sun and Jupiter, 
its shadow is projected on the surface of the planet in the 
same manner as the shadow of the moon is projected on the 
Earth in a solar eclipse. This is called a transit of the shadow. 
and the shadow may be seen to move across the disc of the 
planet as a small round black spot. The entrance of the 
shadow upon the disc is called the ingress, and its depart- 
ure is called its egress. 

4th. When a satellite passes between the Earth and plan- 
et, its disc is projected on that of the planet ; and it may 
sometimes be seen with a good telescope when it is project- 
ed on a portion of the disc either darker or brighter than 
itself. This is called a transit of the satellite. 



180 ASTRONOMY. 

From the preceding phenomena, it results that frequent* 
ly not more than two or three of the satellites are visible- 
sometimes only one satellite is visible; and in a few in- 
stances all four have been invisible for a short time. Such 
a case occurred August 21, 1867. 

315. Longitude determined by observations of the Eclipses, 
— The time of occurrence of the eclipses of Jupiter's satel 
lites is computed several years beforehand and published in 
the Nautical Almanac, and is expressed in Greenwich mean 
time. If, then, the time at which one of them occurs at any 
other station be observed, the difference between the local 
time and that given in the Almanac will be the longitude 
of the place from the meridian of Greenwich. 

Since the light of a satellite decreases gradually while en- 
tering the shadow, and increases gradually on leaving it, the 
observed time of disappearance or reappearance of a satellite 
must depend on the power of the telescope employed, and 
hence this method of determining longitude is not very ac- 
curate. 

316. Velocity of Light. — Soon after the invention of the 
telescope, Roemer, a Danish astronomer, computed a table 
showing the time of occurrence of each eclipse of Jupiter's 
satellites for a period of twelve months. He then observed 
the moments of their occurrence, and compared his observed 
times with the times which he had computed. At the com- 
mencement of his observations the Earth was at E', where 
it is nearest to Jupiter (Fig. 98). As the Earth moved to- 
ward E", the eclipses occurred a little later than the time 
computed. As the Earth moved toward E'", the eclipses 
were more and more retarded, until at E'" they occurred 
more than 16 minutes later than the computed time. While 
the Earth moved from E'" to E' the retardation became less 
and less, until, on arriving at E', the observed time agreed 
exactly with the computed time. 

Now, since the eclipse must commence as soon as the sat- 
ellite enters Jupiter's shadow, the delay in the observed time 
must be due to the time required for the light, which left 
the satellite just before its immersion in the shadow, to reach 



SATURN. 181 

the eye. This retardation amounted to a little over 16 
minutes for a distance equal to the diameter of the Earths 
orbit, which makes the velocity of light 184,000 miles per 
second. 

SATURN. 

317. Period, Distance, etc. — Saturn makes one revolution 
about the sun in 29^ years, but the interval between two 
successive oppositions is 378 days. 

Its mean distance from the sun is 876 millions of miles; 
and, since the eccentricity of its orbit is about -^h? tn i s 
distance is augmented at aphelion and diminished at peri- 
helion by 44 millions of miles. 

Saturn is the largest of all the planets except Jupiter. 
Its equatorial diameter is 74,000 miles, being more than nine 
times that of the Earth, and its volume is nearly 800 times 
that of the Earth. It appears as a star of the first magni- 
tude, with a faint reddish light. 

318. Rotation on an Axis, etc. — Saturn makes one rota- 
tion upon its axis in 10-J- hours, and the inclination of the 
planet's equator to the plane of the ecliptic is 28°. Thus 
the year of Saturn is diversified by the same succession of 
seasons as prevail on our globe. 

The disc of Saturn is not circular, the equatorial diameter 
being y^th greater than the polar. The disc is frequently 
crossed with dark bands or belts parallel to its equator, but 
these belts are much more faint than those of Jupiter. 
These belts indicate the existence of an atmosphere sur- 
rounding the planet, and attended with the same system of 
currents which prevail on Jupiter. 

319. Saturn's Ring. — Saturn is surrounded by a broad 
but thin ring, situated in the plane of its equator, and en- 
tirely detached from the body of the planet. This ring 
sometimes throws its shadow on the body of the planet, on 
the side nearest the sun, and on the other side is partially 
hidden by the shadow of the planet, showing that the ring 
is opaque, and receives its light from the sun. 

The ring is inclined to the plane of the ecliptic at an angle 



182 



ASTRONOMY. 



Fig. 99. 




of 28°, and whik 
the planet moves in 
its orbit round the 
sun, the plane of 
the ring is carried 
parallel to itself. 
The true form of 
the ring is very 
nearly circular; but 
since we never view 
it perpendicularly, 
its apparent form is that of an ellipse more or less eccentric. 
Twice in every revolution — that is, at intervals of 15 years, 
the plane of the ring must pass through the sun ; and the 
ring, if seen at all, must appear as a straight line. As the 
planet advances in its orbit, the ring appears as a very ec- 
centric ellipse. This eccentricity diminishes until Saturn 
has advanced 90° in its orbit, when the minor axis of the 
ellipse becomes equal to about half the major axis, from 
which time the minor axis decreases, until, at the end of half 
a revolution, the ring again appears as a straight line. 

These different positions of the ring are represented in 
Fig. 100, where S represents the sun, MN the orbit of the 



Fig. 100. 



1S5Z { 




me 



H 



D 



186f£ 



18G9 



B 



earth, and A, B, C, D, etc., different positions of Saturn. 
When Saturn is at A, the plane of the ring passes through 
the sun, and only the edge of the ring can be seen, as repre« 



SATURN. 183 

sented in the figure ; when Saturn arrives at B, the ring ap- 
pears as an ellipse ; and when it arrives at C, the minor axis 
of the ellipse is equal to about half the major axis. After 
this the minor axis decreases, and when the planet reaches 
E the ring again appears as a straight line. 

320. Disappearance of the Ming. — The ring of Saturn 
may become invisible from the Earth either because the part 
turned toward the Earth is not illumined by the sun, or be- 
cause the illumined portion subtends no sensible angle. 

1st. When the plane of the ring passes through the sun, 
only the edge of the ring is illumined, and this is too thin 
to be seen by any but the most powerful telescopes. 

2d. When the plane of the ring passes through the Earth, 
the ring, for the same reason, disappears to ordinary tel- 
escopes. 

3d. When the Earth and the sun are on opposite sides of 
the plane of the ring — that is, when the plane of the ring, 
if produced, passes between the Earth and the sun, the dark 
face of the ring is turned toward the Earth, and the ring en- 
tirely disappears. 

The last disappearance of Saturn's ring took place in 1862 ; 
and it will attain its greatest opening in 1870. 

321. Divisions of the Ring. — What we have called Sat- 
urn's ring consists of several concentric rings, entirely de- 
tached from each other. It is uncertain what is the num- 
ber of the rings, but in ordinary telescopes a narrow black 
line can be seen dividing the ring into two concentric rings 
of unequal breadth. Similar fainter lines have been occa- 
sionally remarked on both rings, inducing the suspicion that 
they may be composed of several narrow ones. 

Between the interior bright ring and the planet there has 
been lately detected another dark ring, only discernible in 
powerful instruments ; and it is translucent to such a degree 
that the body of the planet can be seen through it. 

322. Dimensions of the Rings. — The inner dark ring ap- 
proaches within about 8000 miles of the body of the planet. 
The distance from the surface of the planet to the inside of 



184 ASTRONOMY. 

the nearest bright ring is 18,000 miles; the breadth of thia 
ring is 16,000 miles; the interval between the two bright 
rings is 1800 miles ; and the breadth of the exterior ring is 
10,000 miles. The greatest diameter of the outer ring is 
165,000 miles. The thickness of the rings is extremely 
small, and is estimated not to exceed 50 or 100 miles. 

323. What sustains Saturrts Rings? — Saturn's rings are 
sustained in the same manner as our moon is sustained in 
its revolution about the Earth. We may conceive two 
moons to revolve about the Earth in the same orbit as tlu> 
present one, and both would be sustained by the same law 
of attraction. In like manner, three, four, or a hundred 
moons might be sustained. Indeed, we may suppose a se- 
ries of moons arranged around the earth in contact with 
each other, and forming a •complete ring ; they would all be 
sustained in the same manner as our present moon is sus- 
tained. If we conceive these moons to be cemented too;eth- 
er by cohesion, we shall have a continuous solid ring ; and 
the ring must rotate about its axis in the same time as a 
moon, situated near the middle of its breadth, w r ould revolve 
about the primary. From observations made upon bright 
spots seen on the ring of Saturn, Herschel discovered that 
it rotated about an axis passing nearly through the centre 
of the planet in a period of lOh. 32m., and this is the period 
in which a satellite whose distance was equal to the mean 
distance of the particles of the ring would revolve around 
the primary. 

324. Constitution of the Rings. — The discovery of a new 
ring, together with the apparently variable number of the 
divisions of the brighter rings, has suggested the idea that 
the rings consist of matter in the liquid condition. It is 
believed, however, that all the appearances may be explain- 
ed by supposing that the rings consist of solid matter, but 
divided into myriads of little bodies which have no cohe- 
sion, each revolving independently in its orbit as a satel- 
lite to the primary, giving rise to the appearance of a bright 
ring when they are closely crowded together, and a very 
dim one when they are most scattered. This supposition 



SATURN. 185 

*\ T ill explain the phenomena observed about the time of dis- 
appearance of the rings, when the rings frequently present 
the appearance of a broken line of light projecting from each 
side of the planet's disc. 

The faint appearance of the newly-discovered ring, and 
its partial transparency, may he explained by supposing 
that the solid portions of which it is composed are separated 
by considerable intervals, these portions being too small to 
be seen individually. The fact that this inner ring was not 
seen by Sir W. Herschel may be explained by supposing that 
the orbits of some of those portions which once belonged to 
the brighter rings have recently been materially changed, 
and that they now approach much nearer to the body of 
the planet. 

325. Appearance of the Rings from the Planet Saturn, — 
The rings of Saturn must present a magnificent spectacle in 
the firmament of that planet, appearing as vast arches span- 
ning the sky from the eastern to the western horizon. Their 
appearance varies with the position of an observer upon the 
planet. To an observer stationed at Saturn's equator, the 
ring will pass through the zenith at right angles to the me- 
ridian, descending to the horizon at the east and west points. 
If we suppose the observer to travel from the equator to- 
ward the pole, the ring will present the appearance of an 
arch in the heavens, bearing some resemblance in form to a 
rainbow. The elevation of the bow will diminish as the ob- 
server recedes from the equator, and near lat. 63° it will de- 
scend entirely below the horizon. 

326. Satellites of Saturn. — Saturn is attended by eight 
satellites, all of which, except the most distant one, move in 
orbits whose planes coincide very nearly with the plane of 
the rings. The satellites are numbered 1,2,3, etc., in the 
order of their distance from the primary. 

The sixth satellite is the largest, and was discovered in 
1G55. Its distance from the centre of the planet is 770,000 
miles, and the time of one revolution is about 16 days. Its 
diameter is about 3000 miles, and it can be seen with a small 
telescope. 



186 ASTRONOMY. 

The eighth satellite was discovered in 1671. Its distance 
from the centre of the planet is 2,177,000 miles, which is 
nearly twice that of the farthest satellite of Jupiter, and the 
time of one revolution is 79 days. Its diameter is about 
1800 miles. It is subject to periodical variations of bright- 
ness, which indicate that it rotates on its axis in the time of 
one revolution round the primary. This is the only satel- 
lite which takes a longer time to revolve round its primary 
than our moon. 

The fifth satellite was discovered in 1672. Its period of 
revolution is 4-J- days, and its diameter 1200 miles. 

The fourth satellite was discovered in 1684. Its period 
of revolution is 2-f days, and its diameter about 500 miles. 

The third satellite was discovered in 1684. Its period is 
less than two days, and its diameter about 500 miles. 

The second satellite w r as discovered in 1787, and its period 
is 1^ day. 

The first satellite was discovered in 1789, and its period 
is 22 hours. The first and second satellites are so small and 
so near the ring that they can only be seen by the largest 
telescopes under the most favorable circumstances. 

The seventh satellite w r as discovered in 1 848. Its period 
of revolution is 22 days, and it is the faintest of all the 
satellites. 

URANUS. 

327. Discovery ', Period, etc. — Uranus w r as discovered to 
be a planet by Sir W. Herschel in 1781. It had been pre- 
viously observed by several astronomers, and its place re- 
corded as a fixed star, but Herschel was the first person who 
determined it to be a planet. 

Its period of revolution is 84 years, but the interval be- 
tween two successive oppositions is only 370 days. 

Its mean distance from the sun is 1762 millions of miles. 

328. Diameter, etc. — The diameter of Uranus is 33,000 
miles, being about half that of Saturn, and more than four 
times that of the Earth. Its apparent diametefis about 4". 
It is not visible without a telescope except near opposition, 
when, under favorable circumstances, it is barely discernible 
to the naked eye. 



URANUS. —NEPTUNE. 187 




The disc of Uranus appears uniformly bright, without any 
appearance of spots or belts. 

329. Satellites. — Uranus is attended by four satellites, 
whose periods range from 2^ days to 13 days. The two 
outer satellites have been repeatedly observed and are com- 
paratively bright ; the two others are very faint objects, 
and can only be seen in the very best telescopes. The orb- 
its of these satellites are inclined 79° to the plane of the 
ecliptic, and their motions in these orbits are retrograde — 
that is, contrary to that of the Earth in her orbit. 

Sir W. Herschel supposed he had seen six satellites to 
Uranus, but the existence of more than four has not been 
established. 

NEPTUNE. 

330. History of its Discovery. — The existence of this 
planet was detected from the disturbance which it produced 
in the motion of Uranus. It was ascertained that there 
were irregularities in the motion of Uranus which could not 
be referred to the action of the known planets, and in 1845 
the astronomers Le Verrier and Adams attempted to de- 
termine the place and magnitude of a planet which would 
account for these irregularities. They demonstrated that 



lo« ASTRONOMY. 

these irregularities were such as would be caused by an un« 
discovered planet revolving about the sun at a distance 
nearly double that of Uranus, and they pointed out the 
place in the heavens which the planet ought at present to 
occupy. 

On the 23d of September, 1846, Dr. Galle, of Berlin, dis- 
covered the new planet within one degree of the place as- 
signed by Le Verrier. This planet has been called Neptune. 

331. Period, Distance, etc. — It has been found that Nep- 
tune had been repeatedly observed as a fixed star before it 
was recognized as a planet at Berlin. With the aid of these 
observations, its orbit has been very accurately determined. 

Its period of revolution is 164 years, and its mean distance 
from the sun is 2758 millions of miles. Its apparent diam- 
eter is about 2^- seconds, and its real diameter is 36,000 
miles, which is about the same as that of Uranus. 

332. Satellite of Neptune. — Neptune has one satellite, 
which makes a revolution around the primary in six days, 
at a distance about the same as the distance of our moon 
from the earth. The orbit of this satellite is inclined 29° 
to the plane of the ecliptic, and its motion in this plane is 
retrograde. This fact is remarkable, since the only other in- 
stance of retrograde motion among the planets or their sat- 
ellites is in the case of the satellites of Uranus. 

333. Solar System as observed from Neptune. — The ap- 
parent diameter of the sun, as seen from Neptune, is about 
the same as the greatest apparent diameter of Venus seen 
from the earth; and the illuminating effect of the sun at 
that distance is about midway between our sunlight and our 
moonlight. 

As seen from Neptune, the other planets would never ap- 
pear to recede many degrees from the sun. The greatest 
elongation ofUranus would be 40°, of Saturn 18°, and of the 
other planets still less. The nearer planets might perhaps 
be seen by the inhabitants of Neptune as faint stars, and the 
planets would occasionally appear to travel across the sun's 
disc, but these phenomena would bo of rare occurrence. 



COMETS. 189 



CHAPTER XV. 

COMETS. — COMETARY ORBITS. — SHOOTING STARS. 

334. What is a Comet ? — A comet is a nebulous body re- 
volving around the sun in an orbit of considerable eccen- 
tricity. The orbits of all known comets are more eccentric 
than any of the planetary orbits. The most eccentric plan- 
etary orbit is an ellipse, of which the distance between the 
foci is about one third of the major axis. The least eccen- 
tric cometary orbit is an ellipse, of which the distance be- 
tween the foci is more than half the major axis. In conse- 
quence of this eccentricity, and of the faintness of their il- 
lumination, all comets, during a part of every revolution, 
disappear from the effect of distance — that is, they can not 
be observed during their entire revolution about the sun. 

335. Number of Comets. — The number of comets which 
have been recorded since the birth of Christ is over 600, but 
the number belonging to the solar system must be far great- 
er than this. Before the invention of the telescope, only 
those comets were recorded which were conspicuous to the 
naked eye, but within the past fifty years 80 comets have 
been recorded. Their periods are generally of vast length, 
so that probably not more than half the whole number have 
returned twice to their perihelia within the last two thou= 
sand years. Hence we may conclude that if the heavens 
had been closely watched with a telescope two thousand 
years, at least 2500 different comets would have been seen, 
so that the total number of cometary bodies must amount 
to many thousands. 

336. Position of Cometary Orbits. — Comets are confined 
co no particular region of the heavens, but traverse every 
part indifferently, and may be seen near the poles of the 
heavens as well as near the ecliptic. Their orbits exhibit 
every possible variety of position. They have every incli- 



190 ASTRONOMY. 

nation to the ecliptic from zero to 90 degrees, and their mo- 
tion is as frequently retrograde as direct. 

337, Period of Visibility, — The period of visibility of a 
comet depends on its intrinsic brightness, as well as upon its 
position with reference to the earth and sun. This period 
varies from a few days to more than a year, but usually it 
does not exceed two or three months. Only seven comets 
have been observed so long as eight months. 

338. The Coma, Nucleus, Tail, etc. — The general appear- 
ance of a brilliant comet is that of a mass of nebulous mat- 
ter termed the head, condensed toward the centre so as 
sometimes to exhibit a tolerably bright point, which is 
called the nucleus of the comet ; while from the head there 
proceeds, in a direction opposite to the sun, a stream of less 

Fig. 102. 




luminous matter, called the tail or train of the comet. Fre- 
quently the centre of the head exhibits nothing more than 
a higher degree of condensation of the nebulous matter, 
which is not very distinctly defined. The nebulosity which 
surrounds a highly condensed nucleus is called the coma, or 
the nebxdous envelope. 

The tail gradually increases in width and diminishes in 



COMETS. 191 

brightness from the head to its extremity, where it is lost 
in the general light of the sky. 

339. The Nebulous Envelope. — The central nucleus is en- 
veloped on the side toward the sun by a nebulous mass of 
great extent. It does not entirely surround the nucleus 
except in the case of comets which have no tails, but forms 
a sort of hemispherical cap to the nucleus on the side to- 
ward the sun. The tail begins where the nebulous envelope 
terminates, being merely the continuation of the envelope 
in a direction opposite to the sun. Between the nucleus 
and the nebulous envelope there is ordinarily a space less 
luminous than the envelope. The tail has the form of a hol- 
low truncated cone, with its smaller base united to the neb- 
ulous envelope, the sides of the tail being, however, sensibly 
curved, and the convexity being turned toward the region 
to which the comet is moving. That the tail is hollow is 
inferred from the fact that it always appears less bright 
along the middle than near the borders. 

340. The Nucleus. — The nucleus of a comet does not gen- 
erally exceed a few hundred miles in diameter. The great 
comet of 1811 had a nucleus 428 miles in diameter, and 
some have been found less than a hundred miles in diame- 
ter. The majority of comets have no bright nucleus at 
all. 

In a few instances the diameter of the nucleus has been 
estimated at 5000 miles; but it is probable that in these 
cases the object measured was not a solid body, but simply 
nebulous matter in a high degree of condensation. The 
dense nebulosity about the nucleus sometimes exceeds 5000 
miles in diameter, but it is probable that the true nucleus 
never exceeds 500 miles in diameter. 

It is probable that the nucleus of the brightest comets is 
a solid of permanent dimensions, with a thick stratum of 
condensed vapor resting upon its surface. 

341. Dimensions of the Nebulous Envelope. — The head 
of a comet is sometimes more than 100,000 miles in diame- 
ter, and that of the comet of 1811 exceeded a million of 



192 ASTRONOMY. 

miles in diameter. The head of the great comet of 1843 
was about 30,000 miles in diameter. 

The dimensions of the nebulous envelope are subject to 
continual variations. In several instances the envelope has 
diminished in size during the approach to the sun, and di- 
lated on receding from the sun. Such an effect might result 
from the change of temperature to which the comet is ex- 
posed. As the comet approaches the sun, the vapor which 
composes the nebulous envelope may be converted by in- 
tense heat into a transparent and invisible elastic fluid. As 
it recedes from the sun and the temperature declines, this 
vapor may be gradually condensed and assume the form of 
a visible cloud, in which case the visible volume of the comet 
may be increased, although its real volume is diminished. 

342. Changes in the Nebulous Envelope. — When a comet 
has a bright nucleus and a splendid train, the nebulous en- 
velope undergoes remarkable changes as it approaches the 
sun. The nucleus becomes much brighter, and throws out 
a jet or stream of luminous matter toward the sun. Some- 
times two, three, Oi :r»ore jets are thrown out at the same 
time in diverging directions. This ejection of nebulous mat- 
ter sometimes continues, with occasional interruptions, for 
several weeks. The form and direction of these luminous 
streams undergo frequent changes, so that no two successive 
nights present the same appearance. These jets, though 
very bright at their point of emanation from the nucleus, 
become diffuse as they expand, and at the same time curve 
backward from the sun, as if encountering a resistance from 
the sun. These streams combined form the outline of a 
bright parabolic envelope surrounding the nucleus, and the 
envelope steadily recedes from the nucleus. After a few 
days a second luminous envelope is sometimes formed within 
the first, the two being separated by a band comparatively 
dark, and the second envelope increases in its dimensions 
from day to day. A few days later a third envelope is 
sometimes formed, and so on ; while each envelope, as it ex- 
pands, declines in brightness, and finally disappears. Do- 
nates comet in 1858 shoAved seven such envelopes, each sep- 
arated from its neighbor by a band comparatively dark, and 




COMETS. 193 

each steadily receding _^^^^^^^^!; 
from the nucleus. See the 
representation, Fig. 103. 

These envelopes seem to 
be formed of matter driv- 
en off from the nucleus by 
a repulsive force on the 
side next the sun, as light 
particles are thrown off 
from an excited conduct- 
or by electric repulsion; 
and the dark bands sep- 
arating the successive envelopes probably result from a 
temporary cessation or diminished activity of this repulsive 
force. 

343. The Tail. — The tail of a comet is but the prolonga- 
tion of the nebulous envelope surrounding the nucleus. 
Each particle of matter, as it recedes from the nucleus on 
the side next to the sun, gradually changes its direction by 
a curved path, until its motion is almost exactly away from 
the sun. The brightness and extent of the train increase 
with the brightness and magnitude of the envelopes, and the 
tail appears to consist exclusively of the matter of the en- 
velopes driven off by a powerful repulsive force emanating 
from the sun. On the side of the nucleus opposite to the 
sun there is no appearance of luminous streams, and hence 
results a dark stripe in the middle of the tail, dividing it 
longitudinally into two distinct parts. This stripe was for- 
merly supposed to be the shadow of the head of the comet ; 
but the dark stripe remains even when the tail is turned 
obliquely to the sun. It is inferred that the tail is a hollow 
envelope; and when we look at the edges, the visual ray 
traverses a greater quantity of nebulous particles than when 
we look at the central line, whence the central line appears 
less bright than the sides. 

344, Rapid Formation of the Tail. — When a comet first 
appears its light is generally faint, and no tail is perceived. 
As it approaches the sun it becomes brighter, the tail shoots 

I 



194 ASTRONOMY. 

out from the nebulous envelope, and increases from day to 
day ill extent and brightness. It attains its greatest Length 
and splendor soon alter perihelion passage, after which it 
fades gradually away. 

When near perihelion, the tail sometimes increases with 

immense rapidity. The tail of Donati's comet in L858 in- 
creased in length at the rate of two millions of miles per 
day; that of the great comet of 1811, nine millions of miles 
per day; while that of the great comet of 1843, soon after 
passing perihelion, increased 35 millions of miles per day. 

345. Dimensions of t lie Tail — The tails of comets often 
extend many millions of miles. That of 1843 attained a 
length of 120 millions of miles ; that of 181 t had a length 
of over 100 millions of miles, and a breadth of about 15 mil- 
lions; and there have been lour other comets whose tails at- 
tained a length of 50 millions of miles. 

The apparent length of the tail depends not merely upon 
its absolute length, but upon the direction of its axis and its 
distance from the earth. There are on record six comets 
whose tails subtended an angle of at least 90° — that is, whose 
tails would reach from the horizon to the zenith ; and there 
arc about a dozen more whose tails subtended an angle of 
at least 45°. 

346. Position of the Axis of the Tail, — The axis of a 
comet's tail is not, a straight line, and, except near the nu- 
cleus, is not turned exactly from the sun, but, always makes 
an angle with a line joining the sun and comet. This angle 
generally amounts to 10° or 20°, and sometimes even more, 
the tail always inclining from the region toward which the 

comet, proceeds, II* the tail were formed by a repulsive 

force emanating from the sun, which carried particles in- 
8tantly from the comet's head to the extremity of the tail, 
then the axis of the tail would be turned exactly from the 

sun; hut, in hut, the nebulous matter requires several days 
to travel from the comet's head to the extremity ol' the tail, 
and the head meanwhile is moving forward in its orbit, 
whence result both the curvature and backward inclination 
Of the tail. 



COM I I 



195 



We shall assume the existence of a repulsive force by 
which certain particles of a comet are driven off from the 

nucleus, and thai these particles are then acted upon I))' ;i 

more powerful repulsive force emanating from the sun. 
Let S represent the position of the bud, and ABC a per 



Pic 104. 




t i(>n of the comet's orbit, the comet moving in the direction 

of the arrows. Suppose, when the nucleus is at A, a par- 
ticle of matter is expelled from the head of the comet in the 
direction SAD. This particle, in consequence of its inertia, 

will retain the motion in the direction of t he orbit which 

the nucleus had at the time of parting from it; and this 
motion will carry the particle over the line DO, while the 
head is moving from A to C, When the nucleus reaches 
B, .'mother particle is driven off in the direction SBE, This 
particle will also retain the motion which it, had in common 

with the nucleus, mid which will carry it- over EH, while 

the head is moving from r> to C. Thus, when the nucleus 
has reached the point C, the particles which were expelled 
from the head during the period of its motion from A to C 
will all be situated upon the line CHG. This line will bo 
a curve line, tangent at C to the radius vector SC produced. 
and always concave toward the region from which the come, 
proceeds. 



347. J'onit of a Section of the Tail.— A transverse section 
of the tail of a comet is not generally a circle, hut a complex 
curve somewhal resembling an ellipse, in the case of Do- 
nates comet, the longest diameter of this curve was four 
times the least, and in the comet, of 1744 the rat i<> was prob 



196 



ASTRONOMY. 



ably still greater. The longest diameter of the transverse 
section coincides nearly with the plane of the orbit; in other 
words, the tail of a comet spreads out like a fan, so that its 
breadth, measured in the direction of the plane of the orbit, 
is much greater than its breadth measured in a transverse 
direction. 

These facts seem to indicate that all the particles which 
form the tail of a comet are not repelled by the sun with 
the same force. Those particles upon which the repulsive 
force of the sun is greatest, form a tail which is turned al- 
most exactly from the sun ; but those particles upon which 
the repulsive force of the sun is small, form a tail which falls 
very much behind the direction of a radius vector. If, then, 
the head of the comet consists of particles which are un- 
equally acted upon by the sun, the nebulous matter will be 
more widely dispersed in the plane of the comet's orbit than 
in a direction perpendicular to that plane. 



Fig. 105. 



348. Multiple Tails. — When a comet has more than one 

nebulous envelope, 
Art. 342, each of 
them may be pro- 
longed into a train, 
Art. 343 ; and each 
of these tails, being: 
hollow, may be so 
faint near the mid- 
dle as to have the 
appearance of two 
distinct tails. A 
comet with three 
separate envelopes 
might thus appear 
to have six tails, 
like the comet of 
1744 (see Fig. 105). 
If the different en- 
velopes were not 
distinctly separa- 
ted from each oth- 




COMETS. 197 

er, then all the trains would appear to proceed from the 
same nebulous mass, but the whole would present a striped 
appearance, like Donati's comet in 1858. See Fig. 112. 

349. Telescopic Comets. — Comets which are visible only 
in telescopes generally have no distinct nucleus, and are 
often entirely destitute of a tail. They have the appearance 
of round masses of nebulous matter, somewhat more dense 
toward the centre. As they approach the sun they gener- 
ally become somewhat elongated, and the point of greatest 
brightness does not occupy the centre of the nebulosity. 

In some cases the absence of a tail may result from the 
smallness of the comet and the faintness of its light, so that, 
although a tail is really formed, it entirely escapes observa- 
tion. It is, however, remarkable, that those comets whose 
time of revolution is shortest have no tails, but only exhibit 
a slight elongation as they approach the sun, which has 
been supposed to indicate that, by frequent returns to the 
sun, they have lost nearly all that class of particles which 
are repelled by the sun, and which contribute to form the tail. 

350. Small Mass and Density. — The quantity of matter 
in comets is exceedingly small. This is proved by the fact 
that comets have been known to pass near to some of the 
planets and their satellites, and to have had their own mo- 
tions much disturbed by the attraction of these bodies, but 
without producing any visible disturbance in the motion of 
the planets or their satellites. Such was the case with the 
comet of 1770. (See Art, 366.) Since the quantity of mat- 
ter in comets is inappreciable in comparison with the satel- 
lites, while their volumes are enormously large, the density 
of this nebulous matter must be incalculably small. 

The transparency of the nebulosities of comets is still 
more remarkable. Faint telescopic stars have been repeat- 
edly seen through a nebulosity of 50,000 or 100,000 miles 
in diameter, and generally no perceptible diminution of the 
star's brightness can be detected. 

351. Do Comets exhibit Phases? — Comets exhibit no 
phases like those presented by the moon, and which might 



198 ASTRONOMY. 

be expected from a solid nucleus shining by reflected light. 
Some have therefore concluded that comets are self-lumin* 
ous ; but observations with the polariscope have proved that 
comets shine in a great degree by reflected light. The same 
is also proved by the fact that comets gradually become 
dim as they recede from the sun, and they vanish simply 
from loss of light, while they still subtend a sensible angle, 
whereas a self-luminous surface appears equally bright at 
all distances as long as it has a sensible magnitude. 

The nucleus of a comet is too small to exhibit a distinct 
phase, and the nebulosity which surrounds it is so rare as to 
be penetrated throughout by the sun's rays. 

352. Orbits of Comets. — It was first demonstrated by 
Newton that a body projected into space, and acted upon 
by a central force like gravitation, whose intensity decreases 
as the square of the distance increases, must move in one of 
the conic sections — that is, either a parabola, an ellipse, or 
an hyperbola. Several comets are known to move in ellipses 
of considerable eccentricity ; the paths of most comets can 
not be distinguished from parabolic arcs ; while a few have 
been thought to move in hyperbolas. Since the parabola 
and hyperbola consist of tw T o diverging branches of infinite 
length, a body moving in either of these curves could not 
complete a revolution about the sun. It would enter the 
solar system from an indefinite distance, and, after passing 
perihelion, would move off in a different direction never to 
return. Hence bodies moving in parabolas and hyperbolas 
are not periodic ; but comets moving in elliptic orbits must 
make successive revolutions like the planets. 

It is probable that the orbits which are not distinguish- 
able from parabolas are, in fact, ellipses of great eccentricity, 
which differ but little from parabolas in that portion de- 
scribed by the comet while it is visible to us. 

353. Distance of Comets from the Sun. — Some comets, 
when at perihelion, come into close proximity to the sun. 
The comet of 1843 approached within 70,000 miles from the 
sun's surface, and the comet of 1680 came almost equally 
near. On the other hand, the comet of 1729 3 when at its 



COMETS. 199 

perihelion, was distant from the sun 380 millions of miles. 
The perihelia of more than two thirds of the computed orb* 
its fall within the orbit of the earth. 

When at aphelion, Encke's comet is distant from the sun 
only 388 millions of miles, and it completes its entire revo- 
lution in 3^- years. There are also 24 comets whose orbits 
are wholly included within the orbit of Neptune ; but most 
comets recede from the sun far beyond the orbit of Nep- 
tune, to such a distance that it requires many centuries to 
complete a revolution. 

354. How the Period of a Comet is determined. — Since com- 
ets are only seen in that part of their orbit which is near- 
est to the sun, and since, in the neighborhood of perihelion, 
an ellipse, a parabola, and an hyperbola depart but slight- 
ly from each other, it is difficult to determine in which of 
these curves a comet actually moves ; but if the orbit be an 
ellipse, the comet will return to perihelion after completing 
its revolution. If, then, we find that tw r o comets, visible in 
different years, moved in the same path — that is, have the 
same elements — we presume that they were the same body 
reappearing after having completed a circuit in an elliptic 
orbit ; and if the comet has been observed at several re- 
turns, this evidence may amount to absolute demonstration. 

There are 250 different comets whose orbits have been 
determined, and of these 47 have been computed to move in 
elliptic orbits. There are seven comets which have been 
observed at successive returns to the sun, and whose periods 
are therefore well established, viz., Halley's, Encke's, Biela's, 
Faye's, Brorsen's, D' Arrest's, and Winnecke's. See Fig. 106. 

There are also two or three other comets which are pre- 
sumed, to have been observed at tw r o different returns to the 
sun, but the predictions of their return to perihelion arc not 
3^et verified, so that their periods are not fully established. 

Halley's Comet. 

355. About the year 1705, Halley, an eminent English 
astronomer, found that a comet which had been observed 
in 1682 pursued an orbit which coincided very nearly with 
those of comets which had been observed in 1607 and 1531, 



200 



ASTRONOMY. 

Fig. IOC. 




Fig. 107. 




He hence concluded 
that the same comet 
had made its appear- 
ance in these several 
years, and he predict- 
ed that it would again 
return to its perihe- 
lion toward the end 
of 1758 or the begin- 
ning of 1759. 

Previous to its ap- 
pearance, Clairaut, a 
distinguished French 
astronomer, undertook 
to compute the dis- 
turbing effect of the 
planets upon the com- 
et, and predicted that 
it would reach its peri* 



COMETS. 201 

helion within a month of the middle of April, 1759. It ac« 
tually passed its perihelion on the 12th of March, 1759. 

The last perihelion passage took place on the 16th of No- 
vember, 1835, within a few days of the predicted time. 

The period of this comet is about 76 years, but is liable 
to a variation of a year or more, from the effect of the at- 
tractions of the planets. It approaches the sun to within 
about one half the distance of the Earth, and recedes from 
him to a distance considerably greater than that of Nep- 
tune. The inclination of its orbit to the plane of the eclip- 
tic is 18°, and its motion is retrograde. See Fig. 101. 

Enckds Comet. 

356, This comet is remarkable for its short period of rev- 
olution, which is only 3^- years. At perihelion it passes 
within the orbit of Mercury, while at aphe- Fig. ios. 
lion its distance from the sun is fths that 
of Jupiter. The inclination of its orbit to 
the ecliptic is 13°, and its motion is direct. 
Its period was determined by Professor 
Encke, of Berlin, in 1819, on the occasion 
of its fourth recorded appearance. Since 
then it has made 15 returns to perihelion, 
and has been observed at each return. Its last return took 
place in September, 1868. 

357. Indications of a Resisting Medium. — By comparing 
observations made at the successive returns of this comet, 
it is found that, after allowance has been made for the dis- 
turbing action of the planets, the periodic time is continual- 
ly diminishing and the orbit is slowly contracting. The 
diminution amounts to about three hours in each revolu- 
tion. Professor Encke attributed this effect to the action 
of an extremely rare medium, which causes no sensible ob- 
struction to the motions of dense bodies like the planets, 
but which sensibly resists the motion of so light a body as 
a comet. The effect of such a medium must be to diminish 
the velocity in the orbit, and consequently the comet ia 
drawn nearer to the sun, and moves in an orbit lying with- 
in that which would otherwise be described ; its mean dis* 

12 




202 



ASTRONOMY. 



tance from the sun is therefore diminished, and it perform! 
its revolution in less time. If this diminution of the orbit 
should continue indefinitely, the comet must ultimately be 
precipitated upon the sun. 

Encke's comet is the only body at present known % which 
requires us to admit the existence of a resisting medium, 
and, according to Professor Encke, this resistance is not ap- 
preciable beyond the orbit of Venus. This resistance may 
arise from collision with innumerable small bodies similar 
to those which the Earth daily encounters, and which pro- 
duce the phenomena of shooting stars. 

JBielcCs Comet. 

358. In 1826, M. Biela discovered a comet, and found thai 
its orbit was similar to those of the comets of 1772 and 1805 r 
and he concluded that it revolved in an elliptic orbit witl? 
a period of about Of years. At perihelion the distance of 
this comet from the sun is a little less than that of the earth, 
while at aphelion its distance somewhat exceeds that of 
Jupiter. 

The orbit of this comet very nearly intersects the orbil 
of the Earth, and in 1805 the comet passed within six mil 
lion miles of the earth. 



Fig. 109. 



359. T/ie appearance of a Comet depends upon the jiosi- 

tion of the Earth.— 
Comets are intrinsic* 
ally the most lumin* 
ous soon after pass- 
ing perihelion, but 
their apparent sizo 




and brightness ^de* 
>end greatly 



upon 
the position of the 
Earth in its orbit. 
This will appear from 
Fig. 109, which rep- 
resents the orbit of 
the Earth, and also a 
portion of the orbit 



COMETS. 203 

of Biela's comet. If, when the comet is at B, tho Earth 
should be near the same point, the comet would be the 
most conspicuous possible. This case happens when Biela's 
comet passes its perihelion in January. But if, when the 
comet is at B, the Earth should be in the opposite part of its 
orbit, the comet would be in the most unfavorable position 
to be observed, because its distance would be great, and the 
comet would be lost in the sun's rays. This case happens 
when the comet passes its perihelion in July. 

Since, at the successive returns of the same comet to peri- 
helion, the Earth may have every variety of position in its 
orbit, the apparent size and brilliancy of a comet may be 
very different at its different returns to the sun. 

360. Division of BieUCs Comet. — In 1846, this comet pre- 
sented the singular phenome- Fig. no. 
non of a double comet, or two 
distinct comets moving side 
by side. See Fig. 110. The 
orbits of these two bodies were 
found to be ellipses entirely in- 
dependent of each other, and 
during their entire visibility 
in 1846, their distance apart 
was about 200,000 miles. 

This comet reappeared in 
August, 1852, as a double 
comet, the distance of the two bodies from each other being 
about 1,500,000 miles. 

This comet was not seen in 1866, although its perihelion 
passage should have occurred in January, when its position 
is the most favorable for observation. 

It has been found by computation that near the close of 
December, 1845, Biela's comet passed extremely near and 
probably through the stream of November meteors. (Art. 
374.) It has been conjectured that this collision may have 
produced the separation of this comet into two parts ; and 
that, by subsequent encounters in 1859 and 1866, it may 
have been farther subdivided and dissipated, so as to be 
permanently lost to our view. 




204 ASTRONOMY. 

Fane's Comet 

361. In 1843, M. Faye, of the Paris Observatory, discos 
ered a comet, and determined its orbit to be an ellipse with 
a period of only 7-J years. Its succeeding return to peri 
helion was predicted for April 3, 1851, and it arrived within 
about a day of the time predicted. The comet made its 
third appearance in September, 1858, and its fourth appear- 
ance in 1865, and its observed positions agreed almost ex 
actly with those which had been predicted, showing thai 
this body does not encounter any appreciable resistance. 

The distance of Faye's comet from the sun at perihelion 
is 154 millions of miles, and at aphelion 542 millions. This 
comet is remarkable as having an orbit approaching nearer 
in form to the orbits of the planets than any other cometary 
orbit known, its eccentricity being only -j^V 

JBr or serfs Comet. 

362. In February, 1846, Mr. Brorsen, of Denmark, discov- 
ered a telescopic comet, which has been found to revolve 
around the sun in about 5-J years. In March, 1857, it was 
again observed on its return to perihelion ; audits third re- 
turn to perihelion was observed in April, 1868, at which 
time the comet was found within one degree of the place 
previously computed. 

The distance of this comet from the sun at perihelion is 
60 millions of miles, being less than the distance of Venus; 
and at aphelion 516 millions, which is somewhat greater than 
the distance of Jupiter. The orbit of this comet, when pro- 
jected on the ecliptic, is included wholly within that of Biela. 

D^ Arrests Comet. 

363. In 1851, Dr. D'Arrest, of Leipsic, discovered a faint 
telescopic comet whose orbit was computed to be an ellipse, 
having a period of 6.4 years. The comet was observed 
again on its return to perihelion in November, 1857, accord- 
ing to prediction. Owing to its unfavorable position, the 
comet was not seen in 1864, but it is predicted that it will 
return again to perihelion September 22, 1870, under circum* 
stances extremely favorable for observation. 



COMETS. 205 

The distance of this comet from the sun at perihelion is 
107 millions of miles, and at aphelion 524 millions. 

'Winnecke's Cornet. 

364. In 1819, M. Pons, at Marseilles, discovered a comet 
whose orbit was computed to be an ellipse, with a period of 
5.6 years. This comet was rediscovered in 1858 by Dr. 
Winnecke, at Bonn, having made seven revolutions since its 
apparition in 1 819, showing the time of one revolution to be 
5.54 years. Owing to its unfavorable position, this comet 
was not seen in 1863, but it is expected to be seen again in 
1869. 

The distance of this comet from the sun at perihelion is 
70 millions of miles, and at aphelion 505 millions. 

The orbits of the six periodical comets last mentioned 
show a striking resemblance to each other. The direction 
of their motion about the sun is the same as that of the 
planets, and they move in planes not more inclined to the 
ecliptic than the orbits of the asteroids. In the dimensions 
and positions of their orbits, in the degree of their eccen- 
tricity as well as in the direction of their motions, they show 
a family resemblance nearly as decided as that between thu 
diiferent individuals of the group of asteroids. 

The Comet of 1744. 

365. The comet of 1744 was remarkable for the brilliancy 
of its head and for the complexity of its train. When near 
perihelion the head was seen with a telescope at midday, 
and it was seen with the naked eye some time after sunrise. 
The tail also exhibited remarkable curvature, and spread 
out like a fan divided into several branches, presenting the 
appearance of six tails, which extended from 30° to 44° from 
the head of the comet. See Fig. 105. 

The distance of this comet from the sun at perihelion was 
but little more than one half the mean distance of Mercury, 
and the form of the orbit is sensibly parabolic. 

The Comet of 1770. 

366. The comet of 1770 is remarkable for its near ap- 
proach to the Earth and Jupiter, and the consequent changes 



206 ASTRONOMY. 

in the form of its orbit. From the observations made in 
1770, its orbit was computed to be an ellipse, with a period 
of 5-J- years ; still, though a very bright comet, it had not 
been seen before 1770, and has not been seen since. 

By tracing back the comet's path, it was found that in 
1767 it passed near Jupiter, and the attraction of that plan- 
et had changed its orbit from a very large to a very small 
ellipse. Previous to 1767 its perihelion distance was about 
300 millions of miles, at which distance it could never be 
seen from the earth. 

Moreover, this comet has not been seen since 1770. On 
its return to perihelion in 1776, the comet was at a great 
distance from the earth, and continually hid by the sun's 
rays ; and before its next return it again passed so near to 
Jupiter that its orbit was greatly enlarged, and its peri- 
helion distance again became about 300 millions of miles, so 
as to be invisible from the earth. 

367. Mass of this Comet. — In July, 1770, this comet made 
a nearer approach to the earth than any other comet on rec- 
ord, its distance being only ], 400,000 miles. It has been 
computed that if the mass of this comet had been equal to 
that of the Earth, it would have changed the Earth's orbit to 
such an extent as to have increased the length of the year 
by 168 minutes. But astronomical observations show that 
the length of the year has not been increased so much as 
two seconds; from which it follows that the mass of this 
comet can not have been so great as ^Voth of the mass of 
the Earth. 

The mass of the comet must have been smaller than this 
estimate; for, although the comet approached Jupiter with- 
in a distance less than that of his fourth satellite, the mo- 
tions of the satellites were not sensibly disturbed. 

The Great Comet o/1843. 

368. This comet was remarkable for its brilliancy, and for 
its near approach to the sun. On the 2Sth of February it 
was seen at midday close to the sun, and soon after this it 
became a very conspicuous object in the evening twilight. 
Its tail attained a length of 120 millions of miles, and sub 
tended an an^le of from 50 to 70 degrees. 




207 



At perihelion this comet came within 70,000 miles of the 
bua's surface, and the heat to which it was subjected ex- 
plains the enormous length of its tail, and the rapidity with 
which it was formed. 

The best computations indicate that this comet moves in 
an elliptic orbit, with a period of about 1 70 years. 



DonatVs Comet of 1858. 

359. This was the most bril- 
liant comet which has appeared 
since 1843, and was remarkable 
for the changes in its nebulous 
envelopes. (Art. 342.) The tail 
attained a length of 50 millions 
of miles, and subtended an an- 
gle of 60°. The nucleus w^as 
uncommonly large and was in- 
tensely brilliant. Its perihelion 
distance was 50 millions of 
miles; its orbit is elliptical, and 
its period about two thousand 
years. 



Fiff. 112. 




370. Is it possible for a Comet to strike the Earth? — Since 
comets move through the planetary spaces in all directions, 
it is possible that the Earth may some time come in collis- 
ion with one of them. The comet of 1770 passed within 
1,400,000 miles of the earth. The first comet of 1864 pass- 
ed within 600,000 miles of the Earth's orbit ; and Biela's 



208 ASTRONOMY. 

comet passes so near, that a portion of the Earth's orbit 
must at times be included within the nebulosity of the 
comet. 

The consequences which would result from a collision be- 
tween the Earth and a comet would depend upon the mass 
of the comet. If the comet had no solid nucleus, it is prob- 
able that it would be entirely arrested by the earth's at- 
mosphere, and no portion of it might reach the earth's sur- 
face. Shooting stars and aerolites are probably comets, or 
portions of comets so small as to be invisible before pene- 
trating the earth's atmosphere. 

Shooting Stars. 

371. Sometimes, upon a clear evening, we observe a bright 
object, in appearance resembling a planet or a fixed star, 
shoot rapidly across the sky and suddenly vanish. This 
phenomenon is known by the name of shooting star or foil- 
ing star. They may be seen on every clear night, and at 
times follow each other so rapidly that it is quite impossible 
to count them. They generally increase in frequency from 
the evening twilight throughout the night until the morn- 
ing twilight, and when the light of day does not interfere, 
they are most numerous about 6 A.M. 

372. Height, Velocity, etc. — By means of simultaneous 
observations made at two or more stations at suitable dis- 
tances from each other, we may determine their height 
above the earth's surface, the length of their paths, and the 
velocity of their motion. It is found that they begin to be 
visible at an average elevation of 74 miles, and they disap- 
pear at an average elevation of 52 miles. The average 
length of their visible paths is 28 miles. The average ve- 
locity relative to the earth's surface, for the brighter class 
of shooting stars, amounts to about 30 miles per second ; 
and they come in the greatest numbers from that quarter 
of the heavens toward which the earth is moving in its an- 
nual course around the sun. 

373. Meteoric Orbits, etc. — Having determined the veloci- 
ty and direction of a meteor's path with reference to the 



SHOOTING STARS. 209 

earth, we can compute the direction and velocity of the mo- 
tion with reference to the sun. In this manner it has been 
shown that these bodies, before they approached the earth, 
were revolving about the sun in ellipses of considerable 
eccentricity. In some instances the velocity has been so 
great as to indicate that the path differed little from a 
parabola. 

It is thus demonstrated that ordinary shooting stars are 
small bodies moving through space in paths similar to the 
comets ; and it is probable that they do not differ material- 
ly from the comets except in their dimensions, and perhaps, 
also, in their density. 

Their light is probably due to the high temperature re- 
sulting from the resistance of the air to the rapid motion of 
the meteor. It is true that, at the ordinary elevation of 
shooting stars, the air is exceedingly rare ; but the resist- 
ance of this air suffices entirely to destroy the motion of a 
body moving about 30 miles per second, and the heat thus 
developed must be sufficient to melt or disintegrate the 
meteor. 

374. Periodic Meteors of November. — In the year 1833, 
shooting stars appeared in extraordinary numbers on the 
morning of November 13th. It was estimated that they 
fell at the rate of 575 per minute. Most of these meteors 
moved in paths which, if traced backward, would meet in a 
point situated near Gamma, in the constellation Leo. A 
similar exhibition took place on the 12th of November, 1799, 
and there are recorded ten other similar appearances at about 
the same season of the year. 

There was a repetition of this remarkable display of me- 
teors on the morning of November 14th, 1866, when the 
number amounted to 120 per minute; also November 14th, 
1867, when the number of meteors for a short time amount- 
ed to 220 per minute; and November 14, 1868, the display 
of meteors was about equally remarkable. 

375. Period of the November Meteors. — The great dis- 
plays of November meteors recur at intervals of about one 
third of a century, but a considerable display may occur on 



210 



ASTRONOMY. 



Fig. 113. 



OJ3JJX 



^^S 




three consecutive years. It is con* 
eluded that these meteors belong 
to a system of small bodies de- 
scribing an elliptic orbit about the 
sun, and extending in the form of 
a stream along a considerable arc 
of that orbit, and making a rev- 
olution about the sun in 33 years. 



376. The Periodical Meteors of 
August. — Meteors appear in un- 
usual numbers about the 10th of 
August, when the number is five 
times as great as the average for 
the entire year. They seem chief- 
ly to emanate from a fixed point 
in the constellation Perseus. 

The August meteors are be- 
lieved to describe a very large elliptic orbit about the sun, 
extending considerably beyond the orbit of Neptune ; and 
the 4 meteors are spread over the entire circumference of this 
orbit, but not in equal numbers. 

Detonating Meteors. 

377. Ordinary shooting stars are not accompanied by any 
audible sound, although they are sometimes seen to break 
into pieces. Occasionally meteors of extraordinary brillian- 
cy are succeeded by a loud explosion, followed by a noise 
like that of musketry or the discharge of cannon. These 
have been called detonating meteors. 

On the morning of November 15th, 1859, a meteor passed 
over the southern part of New Jersey, and was so brilliant 
that the flash attracted general attention in the presence of 
;ui unclouded sun. Soon after the flash there was heard a 
sencs of terrific explosions, which were compared to the dis- 
charge of a thousand cannon. From a comparison of nu- 
merous observations, it, was computed that the height of 
this meteor when first seen was over GO miles; and when it 
exploded its height was 20 miles. The length of its visible 
path was more than 40 miles. Its velocity relative to the 



AEROLITES. 211 

earth was at least 20 miles per second, but, its velocity rel« 
ative to the sun was about 28 miles per second, indicating 
that it was moving about the sun in a very eccentric ellipse, 
or perhaps a parabola. 

378. Number,Velocitt/j etc. — The number of detonating 

meteors recorded in scientific; journals is over 800. Their 
average height at the instant of apparition is 92 miles, and 
at the instant of vanishing is 32 miles. Their average ve- 
locity relative to the earth is 10 miles per second. 

An unusual number of detonating meteors has been seen 
about November 13th and August 10th. This coincidence, 
taken in connection with the results obtained respecting 
their paths and velocities, leads us to conclude that both be- 
long to the same class of bodies, and that they probably do 
not differ much from each other except in size and perhaps 
in density. The noise which succeeds their appearance is 
probably, in great part, due to the collapse of the air rush- 
ing into the vacuum which is left behind the advancing me- 
teor. No audible sound proceeds from ordinary shooting 
stars, because they are bodies of small size or of feeble dens- 
ity, and are generally consumed while yet at an elevation 
of 50 miles above the earth's surface. 

Aerolites. 

379. Ordinary shooting stars arc consumed or dissipated 
before reaching the denser part of the earth's atmosphere, 
but occasionally one is large enough and dense enough to 
penetrate entirely through our atmosphere and reach the 
surface of the earth. These bodies are called aerolites. 
When they present mainly a stony appearance, they are 
called meteoric stones ; when they are chiefly metallic, they 
are called meteoric iron. Numerous examples of aerolites 
have been recorded. 

380. TheWeston Aerolite. — In December, 1807, a meteor 

of great brilliancy passed oyer the southern pail of Con- 
necticut, and soon after its disappearance there were heard 
three loud explosions like those of a cannon, and there de- 
scended numerous meteoric stones. The entire weight of 



212 



ASTRONOMY. 



all the fragments discovered was at least 300 pounds. Their 
specific gravity was 3.6; their composition was one half 
silex, one third oxide of iron, and the remainder chiefly mag- 
nesia. The length of the visible path of this meteor exceed- 
ed 100 miles, and its velocity relative to the earth was about 
15 miles per second. 

381. Number and Composition of Aerolites, — There are 
19 well-authenticated cases in which aerolites have fallen 
in the United States, and their aggregate weight is 1250 
pounds. The entire number of known aerolites, the date 
of whose fall is well determined, is 262, and there are many 
more the date of whose fall is uncertain. Besides these 
there have been found 86 masses, which, from their peculiar 
composition, are believed to be aerolites, although the date 
of their fall is unknown. The weight of these masses va- 
ries from a few pounds to several tons. 

Aerolites are composed of the same elementary substances 
as occur in terrestrial minerals, not a single new element 
having been found in their analysis ; yet they differ greatly 
in the proportions of these ingredients. Some contain 96 
per cent, of iron, while others contain less than one per cent. 
The appearance of aerolites is quite peculiar, and the group- 
ing of the elements — that is, the compound formed by them, 
is so peculiar as to enable us, by chemical analysis, to dis- 
tinguish an aerolite from any terrestrial substance. 



382. Widmannstdten Figures. — Meteoric iron possesses a 

Fie:. 114 




AEROLITES. 213 

highly crystalline structure. If the surface he carefully 
polished, and the mass be heated to a straw yellow, after 
cooling, the surface will be covered with lines and streaks 
having considerable regularity in their position. Often we 
find a system of lines nearly parallel with each other, inter- 
sected by others at angles of sixty degrees, forming trian- 
gles nearly equilateral. The same figures can also be de- 
veloped by the use of acids. 

Ordinary iron will not exhibit these figures, but iron 
melted directly out of some volcanic rocks does exhibit 
them. 

383, Origin of Aerolites. — It has been conjectured that 
aerolites are masses ejected from terrestrial volcanoes. This 
supposition is inadmissible, because the greatest velocity 
with which stones have ever been ejected from volcanoes 
is less than two miles per second, and the direction of this 
motion must be nearly vertical, while aerolites frequently 
move in a direction nearly horizontal, and with a velocity 
of several miles per second. 

It has been conjectured that aerolites have been ejected 
from volcanoes in the moon with a velocity sufficient to 
carry them out of the sphere of the moon's attraction into 
that of the earth's attraction. It has been estimated that 
if an indefinite number of bodies were projected from the 
moon in all directions and with different velocities, not one 
in a million would have precisely that direction and that 
rate of motion which would be requisite to allow it to reach 
the earth. We can not, then, admit that lunar volcanoes 
have ejected rocks in such quantities as to account for the 
known aerolites, especially as the lunar volcanoes are to all 
appearance nearly, if not entirely extinct. 

384. Conclusions. — A comparison of all the facts which 
are known respecting shooting stars, detonating meteors, 
and aerolites, leads to the conclusion that they are all mi- 
nute bodies revolving like the comets in orbits about the 
sun, and are encountered by the Earth in its annual motion. 
The visible path of aerolites is somewhat nearer to the 
earth's surface than that of ordinary shooting stars, a re* 



214 ASTRONOMY. 

suit which may be ascribed to their greater size or greater 
density. It is probable also that the velocity with which 
they describe their visible path is somewhat less than that 
of ordinary shooting stars, a result which may be due to 
their descending into an atmosphere of greater density, 
which causes, therefore, greater resistance to their motion,, 



THE FIXED STARS. 215 



CHAPTER XVI. 

THE FIXED STARS THEIR DISTANCE AND THEIR MOTIONS. 

385. What is a Fixed Steer ? — The fixed stars are so call* 
ed because from century to century they preserve almost 
exactly the same positions with respect to each other. Many 
of the stars form groups which are so peculiar that they are 
easily identified, and the relative positions of these stars are 
nearly the same now as they were two thousand years ago. 
Accurate observations, however, have shown that great 
numbers of them have a slow progressive motion along the 
sphere of the heavens. This change of place is quite small, 
there being only about 30 stars whose motion is as great as 
one second in a year, and generally the motion is only a few 
seconds in a century. 

386. How the Fixed Stars are classified. — The stars are 
divided into classes, according to their different degrees of 
apparent brightness. The brightest are termed stars of the 
first magnitude ; those which are next in order of bright- 
ness are called stars of the second magnitude, and so on to 
stars of the sixth magnitude, which includes all that can be 
distinctly located by the naked eye. Stars smaller than the 
sixth magnitude are called telescopic stars, being invisible 
without the assistance of the telescope. Telescopic stars 
are classified in a similar manner down to the twelfth, and 
even smaller magnitudes. 

According to the best authority, the number of stars of 
the first magnitude is 20; of the second magnitude, 34; of 
the third, 141 ; fourth, 327 ; fifth, 959 ; and sixth, 4424 ; 
making 5905 stars visible to the naked eye. Of these, only 
about one half can be above the horizon at one time, and it 
is only on the most favorable nights that stars of the sixth 
magnitude can be clearly distinguished by the naked eye. 

The number of stars of the seventh magnitude is estimated 
at 13,000 ; of the eighth magnitude, 40,000 ; and ninth mag- 




216 ASTRONOMY. 

nitude, 142,000; making about 200,000 stars from the first 
to the ninth magnitude. It is estimated that the number 
of stars visible in Herschel's reflecting telescope of 18 inches' 
aperture was more than 20 millions, and the number visible 
in larger telescopes is still greater. 

387. Comparative Brightness of the Stars, — Sir W. Her- 
schel estimated that the average brightness of stars from 
the first to the sixth magnitude might be represented ap- 
proximately by the numbers 100, 25, 12, 6,2, 1. Fig. 115 is 

Ficr.ii5 designed to give an 

idea of the relative 
brightness of stars of 
the first six magni- 
tudes. 

It is probable that 
these varieties of 
brightness are chiefly caused by difference of distance rath- 
er than by difference of intrinsic splendor. Those stars 
which are nearest to our solar system appear bright in con- 
sequence of their proximity, and are called stars of the first 
magnitude; those which are farther off are more numerous 
and appear less bright ; and thus, as the distance of the stars 
increases, their apparent brightness diminishes, until at a cer- 
tain distance they become invisible to the naked eye. 

388. Have the Fixed Stars a sensible Disc? — When Ju- 
piter or Saturn is viewed with a telescope, the planet ap- 
pears with a considerable disc, like that which the moon 
presents to the naked eye, but it is different even with the 
brightest of the fixed stars. A bright star, viewed by the 
naked eye, generally appears to subtend an appreciable an- 
gle, but the telescope exhibits it as a lucid point of very 
small diameter, even when the highest magnifying powers 
are employed. With a power of 6000, the apparent diame- 
ter of the star seems less than with lower powers. 

The term magnitude, applied to the fixed stars, designates 
simply their relative brightness. None of the stars have any 
measurable magnitude at all. The quantity of light which 
they emit leads us to infer, however, that their absolute di* 



THE FIXED STARS. 217 

ameters are very great, and hence we conclude that their 
distance is so enormous that their apparent diameter, seen 
from the earth, is 6000 times less than the smallest angle 
which the naked eye is capable of appreciating. 

389. Division into Constellations. — In order to distinguish 
the fixed stars from each other, they have been divided into 
groups called constellations. These constellations are imag- 
ined to form the outlines of figures of men, of animals, or of 
other objects. In a few instances the arrangement of the 
stars may be conceived to bear some resemblance to the ob- 
ject from which the constellation is named, as, for exam- 
ple, the Swan and the Scorpion, while in most instances no 
such resemblance can be traced. This mode of grouping 
the stars is of great antiquity, and the names given by the 
ancients to individual constellations are still retained. 

39(K Names of the Constellations. — The constellations are 
divided into three classes — northern constellations, southern 
constellations, and constellations of the zodiac. 

There are twelve constellations lying upon the zodiac, and 
hence called the zodiacal constellations, viz., Aries, Taurus, 
Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Cap- 
ricornus, Aquarius, and Pisces. These are also the names 
of the signs of the zodiac, or portions of 30° each into which 
the ecliptic has been divided ; but the effect of precession, 
which throws back the place of the equinox 50" a year, has 
caused a displacement of the signs of the zodiac with respect 
to the constellations bearing the same names. The vernal 
equinox, or first point of the sign Aries, is near the be- 
ginning of the constellation Pisces, the sign Taurus is in the 
constellation Aries, and so on, the signs having retreated 
among the stars 30° since the present division of the zodiac 
was adopted. 

The principal constellations north of the zodiacal constel- 
lations are : 

Andromeda. Cassiopeia. Draco. Perseus. 

Aquila. Cepheus. Hercules. Serpentarius. 

Auriga. Corona Borealis. Lyra. Ursa Major. 

Bootes. Cygnus. Pegasus. Ursa Minor. 

K 



218 ASTRONOMY. 

The principal constellations south of the zodiacal constel 
lations are : 

Argo Navis. Cetus. Lupus. 

Canis Major. Crux. Orion. 

Can is Minor. Eridanus. Phoenix. 
Centaurus. Hydra. Piscis Australis. 

Others will be found upon celestial globes and charts, 
raising the total number of constellations generally recog- 
nized by astronomers to eighty-six. 

391. How individual Stars are designated, — Many of the 
brighter stars had proper names assigned them at a very 
early date, as Sirius, Arcturus, Regulus, Rigel, etc., and by 
these names they are still commonly distinguished. 

In 1604, Bayer, a German astronomer, published maps of 
the heavens, in which the stars of each constellation were 
distinguished by the letters of the Greek and Roman alpha- 
bets, the brightest being denoted by a, the next /3, and so 
on. Thus Alpha (a) Lyra3 denotes the brightest star in the 
constellation Lyra, Beta (/3) Lyra3 the second star, and so on. 

Flamsteed, the first astronomer royal at Greenwich, dis- 
tinguished the stars of each constellation by the numerals 
1, 2, 3, etc., in the order of their right ascensions. 

392. liemarkable Constellations enumerated, — One of the 
most conspicuous constellations in the northern firmament 
is Ursa Major, or the Great Bear, in which we find seven 
bright stars, which may easily be conceived to form the 
outline of a dipper with a curved handle, four of the stars 
forming the bowl and three the handle. The two stars on 
the side of the bowl opposite to the handle are called the 
pointers, because a straight line drawn through them passes 
nearly through the pole star. The dipper is within the cir- 
cle of perpetual apparition at New York, and hence is visi- 
ble at all seasons of the year, although in different positions 
as it revolves around the pole. 

The constellation Ursa Minor contains seven small stars, 
which may also be conceived to form the outline of a small 
dipper, which occupies a reversed position from that of the 
Great Dipper, the pole star forming the extremity of the 
handle. 



THE FIXED STARS. 



210 



The constellation Cassiopeia presents five stars of the third 
magnitude, which, with one or two smaller ones, may be con- 
ceived to form the outline of a chair. It is situated on the 
opposite side of the pole from the Great Dipper. The prin- 
cipal stars of these three constellations are represented in 
Fig. 2, page 15. 

The square of Pegasus is formed by four bright stars sit- 
uated at the angles of a large square about 15° upon each 
side. The equinoctial coiure passes very nearly through 
the two most easterly stars of this square. 

In the constellation Cygnus are five stars so arranged as 
to form a large and regular cross, the one at the northern 
extremity being a star of the first magnitude. 

In the constellation Leo Fig. 116. 

are six bright stars, present- 
ing the form of a sickle; Reg- 
ulus, a star of the first mag- 
nitude, being at the extremi- 
ty of the handle. 

In the head of Taurus are 
several stars called the Hy- 
adcs, presenting the outline 
of the letter V ; Aldebaran, 
a ruddy star of the first mag- 
nitude, being situated at the 
most eastern extremity of 
the letter. About 12° to the 
northwest is a group of stars 
called the Pleiades. The na- 
ked eye discovers six or seven 
stars, but in the telescope up- 
ward of 200 are visible. 

The constellation Orion presents four bright stars in the 
form of a long quadrangle, near the middle of which are 
three bright stars arranged at equal distances in a straight 
line, pointing on the east side to Sirius, the most splendid 
star in the heavens, and on the west side to the Hyades and 
the Pleiades. These three stars are called the belt of Orion, 
and sometimes the Ell and yard. See Fig. 116. 




220 ASTRONOMY. 

393. Catalogues of Stars. — Various catalogues of stars 
have been formed, in which are indicated their right ascen- 
sions and declinations, and sometimes their longitudes and 
latitudes. Hipparchus, 128 years before the Christian era, 
constructed the first catalogue of stars of which we have 
any knowledge. His catalogue included 1022 stars. Mod- 
ern catalogues contain over 200,000 stars. 

394. Periodic Stars. — Some stars exhibit periodical 
changes of brightness, and are therefore called periodic 
stars. One of the most remarkable of this class is the star 
Omicron Ceti, commonly called Mira, or the wonderful star. 
This star retains its greatest brightness for about two weeks, 
being then usually a star of the second magnitude. It then 
gradually decreases, and in about two months ceases to be 
visible to the naked eye, and in about three months more 
becomes reduced to the ninth or tenth magnitude. After 
remaining invisible to the naked eye for six or seven months, 
it reappears, and increases gradually for two months, when 
it recovers its maximum splendor. It generally goes through 
all its changes in 332 days, but this period has fluctuated 
from 317 to 350 days. 

Another remarkable periodic star is Algol, in the constel- 
lation Perseus. For a period of about 61 hours it appears 
as a star of the second magnitude, after which it begins to 
diminish in brightness, and in less than four hours is reduced 
to a star of the fourth magnitude, and thus remains about 
twenty minutes. It then begins to increase, and in about 
four hours more it recovers its original splendor, going 
through all its changes in 2d. 20h. 49m. 

There are more than 100 stars known to be variable to a 
greater or less extent. The periods of these changes vary 
from a few days to many years. 

395. Temporary Stars. — Several instances are recorded 
of stars appearing suddenly in the heavens where none had 
before been observed, and afterward fading gradually away 
without changing their positions among the other stars. 
Such a star appeared in 1572 in the constellation Cassiopeia. 
When brightest it surpassed Jupiter, and was distinctly vis- 



THE FIXED STARS. 221 

ible at midday. In sixteen months it entirely disappeared, 
and has not been seen since. 

A similar example was recorded by Hipparchns 125 B.C. ; 
another in 389 A.D., in the constellation Aquila; others oc- 
curred in the years 949, 1264, 1604, 1670, and 1848. 

In the year 1866, a star in Corona Borealis, which some 
years ago was of the ninth magnitude, suddenly flashed up 
and shone as a star of the second magnitude. In a week it 
changed to the fourth magnitude, and in a month afterward 
it returned to the ninth magnitude. 

It is possible that the temporary stars do not differ from 
the periodic stars except in the length of their periods. 

396. Explanation of Periodic Stars. — The phenomena of 
periodic stars have been explained, 1st, by supposing that 
they have the form of thin flat discs, and, by rotation upon 
an axis, present to us their edge and their flat side alternate- 
ly, thereby producing corresponding changes of brightness. 
This hypothesis will not explain the sudden changes in the 
brightness of Algol, nor the inequality in the periods of 
Mira. 

2d. It has been supposed that a dark opaque body may 
revolve about the variable star so as at times to intercept 
a portion of its light. This hypothesis will explain the gen- 
eral phenomena of Algol, but it will not explain the long- 
continued obscuration of Mira. 

3d. It has been supposed that a nebulous body of great 
extent may revolve around the variable star so as at times 
to intercept a portion of its light. This hypothesis may be 
made to accommodate itself so as to explain the phenomena 
of most of the periodic stars. 

4th. The variable star may not be uniformly luminous 
upon every part of its surface, but, by rotation upon an axis, 
may occasionally present to the earth a disc partially cov- 
ered with dark spots, and shining therefore with a dimmer 
light. This hypothesis will not explain the sudden changes 
in the brightness of Algol, nor will it explain the fluctua- 
tions in the period of Mira, or in the maxima and minima 
of its brightness, unless we admit that the dark spots upon 
its surface are variable, like the dark spots upon our sun. 



222 ASTRONOMY. 

If we suppose that spots are periodically developed upon 
the surface of the variable star similar to those which are 
observed upon our sun, but of vastly greater extent, the 
phenomena of most of the variable stars may be explained. 

397. Distance of the Fixed Stars. — The following consid- 
eration proves that the distance of the fixed stars from the 
earth must be immense. The Earth, in its annual course 
around the sun, revolves in an orbit whose diameter is 183 
millions of miles. The station from which we observe the 
stars on the 1st of January is distant 183 millions of miles 
from the station from which we view them on the 1st of 
July ; yet, from these two remote points, the stars are seen 
in the same relative positions and of the same brightness, 
proving that the diameter of the Earth's orbit must be a 
mere point compared with the distance of the nearest stars. 

398. Annual Parallax, — The greatest angle which the 
radius of the Earth's orbit subtends at a fixed star is called 
its annual parallax. If the annual parallax of a star were 
known, we could compute its distance from the earth, for 
we should know the angles and one side of a right-angled 
triangle, from which the other sides could be computed. 
If a fixed star had any appreciable parallax, it could be de- 
tected by a comparison of the places of the star as observed 
at opposite seasons of the year. Such observations have 
been made upon an immense number of stars, but, until re- 
cently, none of them have shown any measurable parallax. 
These observations are made with such accuracy that if the 
parallax amounted to so much as one second, it could not 
have escaped detection. Hence we conclude that the an- 
nual parallax of every fixed star which has been carefully 
observed is less than one second. 

399. Parallax of Alpha Centauri. — Observations made 
upon the star Alpha Centauri, one of the brightest stars of 
the southern hemisphere, indicate an annual parallax of 
f^ths of a second. Having determined the parallax, we 
compute the distance of the star by the proportion 

sin. 0".92 : 1 :: 92 millions of miles : the distance of the star, 



THE FIXED STAItS. 223 

which is found to be twenty millions of millions of miles. 
This distance is so immense that a ray of light, which would 
make the circuit of our globe in one eighth of a second, re- 
quires more than three years to travel from this star to the 
earth. We do not see the star as it actually is, but as it 
was more than three years ago. Hence, if this star were 
obliterated from the heavens, we should continue to see it 
for more than three years after its destruction; yet Alpha 
Centauri is probably our nearest neighbor among the fixed 
stars. 

400. How differences of Parallax may be detected. — This 
method consists in finding the difference between the paral- 
laxes of a given star and some other star of much smaller 
magnitude, which is therefore supposed to be at a much 
greater distance. This difference is found by measuring 
with a micrometer the annual changes in the distance of 
the two stars, and in the position of the line which joins 
them. The difference of the parallaxes will differ from the 
absolute parallax of the nearest star by only a small part of 
its whole amount. 

By this indirect method a much smaller angle of parallax 
can be detected than by the direct method employed in Art. 
398, for the angular distance between two neighboring stars 
can be measured within a small fraction of a second; and, 
since both stars are seen in nearly the same direction, they 
will be equally affected by refraction, aberration, precession, 
and nutation. The relative situation of the two stars is 
therefore independent of most of the errors that are in- 
evitably committed in determining the absolute places of 
the stars by means of their right ascensions and declina- 
tions. 

401, Peirallax of 61 Cygni. — By the method here indi- 
cated, the parallax of the star 61 Cygni was determined by 
the great astronomer Bessel. Observations of the same star, 
since made by several other astronomers, give nearly the 
same result. The mean of all the observations is 0".45, in- 
dicating a distance of 42 millions of millions of miles, a space 
which light would require seven years to traverse. 



224 ASTRONOMY. 

402. Parallax of other Stars. — No other star has yet been 
found whose parallax exceeds about one quarter of a second. 
Sirius and Alpha Lyrae have apparently a parallax of about 
a quarter of a second, and observations have indicated about 
an equal parallax in four other small stars. All the other 
stars of our firmament are apparently at a greater distance 
from us ; and if the distance of the nearest stars is so great, 
we must conclude that those faint stars, which are barely 
discernible in powerful telescopes, are much more distant. 
Hence we conclude that we do not see the stars as they 
now are, but as they were years ago — perhaps, in some in- 
stances, with the rays which proceeded from them several 
thousand years ago. The changes which we observe in the 
periodic and temporary stars do not indicate changes actual- 
ly going on in the stars at the time of the observations, but 
rather those which took place years — perhaps centuries ago. 

403. Magnitude of the Fixed Stars. — The fixed stars must 
be self-luminous, for no light reflected from our sun could 
render them visible at such enormous distances from us. 
Indeed, it is demonstrable that many of the fixed stars actu- 
ally emit as much light as our sun. It is estimated that 
the light of our sun is 450,000 times greater than that of 
the full moon, and that the light of the full moon is 13,000 
times greater than that of Sirius — that is, the light of the 
sun is about 6000 million times greater than that of Sirius. 
Since the quantity of light which the eye receives from a 
star varies inversely as the square of its distance, and since 
the distance of Sirius is 800,000 times that of the sun, it fol- 
lows that, if Sirius were brought as near to us as the sun, 
its light would be 640,000 million times as great as it ap- 
pears at present — that is, the light emitted by Sirius is a 
hundred times that emitted by our sun. 

A similar comparison shows us that Alpha Lyra3 emits 
more light than our sun, and probably the same is true of 
many other of the fixed stars. We may also infer that 
many of the stars are larger than our sun — that is, are more 
than a million of miles in diameter, otherwise the intensity 
of their illumination must be much greater than that of our 
sun. The fixed stars, therefore, are not mere brilliant points 



THE FIXED STABS. 225 

of light, but material bodies of vast size and intensely lu- 
minous — that is, they are suns; and our own sun appears 
so conspicuous in size and brilliancy only because it is com- 
paratively near to us. 

404. Physical Constitution of the Stars. — When the light 
of a fixed star is passed through a prism, it exhibits a spec- 
trum bearing a general resemblance to that of our sun, but 
crossed by a system of dark lines, some of which are com- 
mon to nearly all the stars, while others belong only to par- 
ticular stars. The position of these lines is considered as 
proving that several elementary substances which are com- 
mon upon the earth are also found in the atmospheres of the 
fixed stars. The substances most widely diffused among the 
stars are sodium, magnesium, iron, and hydrogen. These 
observations lead to the conclusion that the stars have a 
physical constitution analogous to that of our sun, and, like 
it, contain several elementary forms of matter which enter 
into the composition of the earth. 

405. Proper Motion of the Stars. — After allowing for the 
effects of precession, aberration, and nutation upon the posi- 
tion of the stars, it is found that many of them have a pro- 
gressive motion along the sphere of the heavens from year 
to year. This motion is called their proper motion. The 
velocity and direction of this motion continue from year to 
year the same for the same star, but are very different for 
different stars. One star of the seventh magnitude is trav- 
eling thus at the rate of seven seconds in a year. The star 
61 Cygni, whose parallax has been determined (Art. 401), is 
moving at the rate of five seconds annually. The star Alpha 
Centauri has a proper motion of nearly four seconds annual- 
ly, and most of the brighter stars of the firmament have a 
sensible proper motion. The result of this motion is a slow 
but constant change in the figures of the constellations. In 
the case of several stars this change in 2000 years has 
amounted to a quantity easily perceived by the naked eye. 
The proper motion of Arcturus in 2000 years has amounted 
to more than one degree; that of Sirius andProcyon to two 



thirds of a degree. 



K2 



226 ASTRONOMY. 

406. Cause of this proper Motion. — The proper motion 
of a star may be ascribed to two different causes. Either 
the star may have a real motion through space, such as it 
appears to us, or this apparent motion may be caused by a 
real motion through space of the sun, attended by the plan- 
ets, this motion being in a direction opposite to the appar- 
ent motion of the star. On extending the inquiry to a great 
number of stars, we find that both causes must be in exist- 
ence ; that the solar system is traveling through space, and 
thus produces an apparent displacement of all the nearer 
stars, while some, and probably all the stars, have a real mo- 
tion through space. 

407. Motion of the Solar System through Space. — If we 
suppose the sun, attended by the planets, to be moving 
through space, we ought to be able to detect this motion 
by an apparent motion of the stars in a contrary direction, 
as when an observer moves through a forest of trees, his 
own motion imparts an apparent motion to the trees in a 
contrary direction. The stars which are nearest to us would 
be most affected by such a motion of the solar system, but 
they should all appear to recede from A, that point of the 



Fig. 117. 


Fig. 118. 


v * * * 


* 


~- * A 


*-^> B 


' I V. 





% 



heavens toward which the sun is moving, while in the oppo- 
site quarter, B, the stars would become crowded more close- 
ly together. 

408, Direction of the Sim's Motion. — In 1 783, Sir William 
Herschel announced that a part of the proper motion of the 
fixed stars could be explained by supposing that the sun 
has a motion toward a point in the constellation Hercules. 
More recent and extensive investigations have not only es- 



THE FIXED STARS. 227 

tablished the fact of the solar motion, but likewise indicated 
a direction very nearly the same as that assigned by Her- 
schel, viz., toward the star p Herculis. Struve estimates 
that the motion of the sun in one year is about 150 millions 
of miles, which is about one fourth of the velocity of the 
Earth in its orbit, or five miles per second; but Airy makes 
the velocity of our solar system about twenty-seven miles 
per second. 

409. Motion of Revolution of the Stars. — It is probable 
that the solar system does not advance from age to age in 
a straight line, but that it revolves about the centre of grav- 
ity of the group of stars of which it forms a member. This 
centre of gravity is probably situated in the principal plane 
of the Milky Way; and if the orbit of the sun is nearly cir- 
cular, this centre must be about 90° distant from p Herculis, 
the point toward which the solar system is moving — that is, 
in the constellation Perseus. Maedler conjectured that the 
brightest star in the Pleiades was the central sun of our firm- 
ament, but without sufficient reason. The orbit of the so- 
lar system is probably so large that ages may elapse before 
it will be possible to detect any change in the direction of 
the sun's met ion. 

410. Velocity of proper Motion of the Stars. — For a star 
situated at right angles to the direction of the sun's motion, 
and placed at the mean distance of stars of the first magni- 
tude, it is estimated that the angular displacement due to 
the sun's motion is one third of a second per year. Hence 
we conclude that when the proper motion of a star exceeds 
this amount, the excess must be due to a real motion of the 
star in space. In the case of the star 61 Cygni, nearly 5 " 
of its annual proper motion must result from an actual mo- 
tion in space, which motion has been computed to be at least 
42 miles per second. In a similar manner we find that many 
other of the fixed stars have a motion in space more rapid 
than that of our sun. 

411. Double Stars. — Many stars which, to the naked eye 
or with telescopes of small power, appear to be single, when 



228 



ASTRONOMY. 



examined with telescopes of greater power are found to con- 
sist of two stars in close proximity to each other. These 
are called double stars. Some of these are resolved into sepa- 
rate stars by a telescope of moderate power, as Castor, which 
consists of two stars of the third or fourth magnitude, at the 
distance of 5" from each other. Many of them, however, 
can only be separated by the most powerful telescopes. 



Fig. 119. 



1 1 Monoc. £ Cancri. 




Some stars, which to ordinary telescopes appear only 
double, when seen through more powerful instruments are 
found to consist of three stars, forming a triple star ; and 
there are also combinations of four, five, or more stars in 
close proximity, forming quadruple, quintuple, and multiple 
stars. Only four double stars were known until the time 
of Sir W. Herschel, who discovered upward of 500, and later 
observers have extended this number to 6000. 

Double stars are divided into classes according to the dis- 
tance between the two components, those in which the dis- 
tance is least forming the first class. 



412. Comparative Size. — In some instances the two com- 
ponents of a double star are of equal brilliancy, but general- 
ly one star is brighter than the other. This inequality fre- 
quently amounts to three or four magnitudes, occasionally 
to seven or eight ; and Sinus, the brightest star of the heav- 
ens, is attended by a minute companion-star estimated to be 
of the fourteenth magnitude. 

413. Color of the Stars. — Many stars shine with a colored 
light. Thus the light of Sirius is white, that of Aldebaran 
is red, and that of Capella is yellow. 

In numerous instances, the two components of a double 
star shine with different colors, and frequently these colors 
are complementary to each other — that is, if combined, they 



THE FIXED STARS. 229 

would form white light. Combinations of blue and yellow 
or green and yellow are not uncommon, while in fewer cases 
we find one star white and the other purple, or one white and 
the other red. In several instances each star has a rosy light. 

414. Stars optically Double.— -If two stars are nearly in the 
same line of vision, though one is vastly more distant from 
us than the other, they will form a star optically double, or 
one whose components appear in close proximity, simply in 
consequence of the direction from which they are viewed. 
Thus the two stars A and B, seen from the earth at E, will 
appear in close proxim- 

Fie 1^0 

ity, although they may A 

be separated by an in- 2 ~ — = -^= —-% 

terval greater than the B 

distance of the nearest from the earth. If the stars were 
scattered fortuitously over the firmament, the chances are 
against any two of them having a position so close to each 
other as 4", yet many such cases of proximity are known to 
exist. It is probable, then, that in most cases the two com- 
ponents of a double star are at about the same distance 
from the sun. 

415. Binary Stars. — In the year 1780, Sir W. Herschel 
undertook an extensive series of observations of double 
stars, measuring the apparent distance of the components 
from each other, and also their relative position. By this 
means he hoped to be able to detect an annual variation, de- 
pending upon parallax as explained in Art. 400. He found, 
indeed, a change in the distance and relative position of the 
two components, but this change could not be ascribed to 
the Earth's motion about the sun. He ascertained that the 
change was produced by a motion of revolution of one star 
around the other, or of both around their common centre of 
gravity, and he announced that there are sidereal systems 
composed of two stars revolving about each other in regu- 
lar orbits. These stars are termed physically double, or 
binary stars, to distinguish them from other double stars in 
which no such periodic change of position lias been discov- 
ered. 



230 



ASTRONOMY. 




416. Periods and Orbits of Binary Stars. — The orbits of 
several of the binary stars and the lengths 
of their periods have been satisfactorily de- 
termined. The orbits are ellipses of con- 
siderable eccentricity, and the periods vary 
from 36 years to many centuries. In Fig. 
121 the dotted line represents the apparent 
orbit of one of the stars about the other, 
while the black line represents the form of 
the actual orbit as computed. The major 
axis of the ellipse is 7", and the period of 
revolution is 145 years. The star Alpha 
Centauri consists of two components, one 
of the first, the other of the second mag- 
nitude, which revolve about each other in 

an ellipse whose major axis is about 30", and period about 
80 years. 

417. Number of the Binary Stars. — There are 467 double 
stars, in which observations have indicated a change in their 
relative positions, and which are therefore shown to be bi- 
nary stars. The shortest period yet found for any binary 
star is 36 years ; there are only eight whose periods are less 
than a century; there are 142 whose periods are less than 
a thousand years ; while the periods of 325 apparently ex- 
ceed a thousand years. When the motion is so slow, ob- 
servations must be extended over a long interval of time to 
determine satisfactorily the period of an entire revolution. 
It is probable that a large majority of the double stars will 
hereafter be proved to be physically connected. 

418. Actual Distance betioeen the Components of a Binary 
Star. — If we knew the distance of a binary star from the 
earth, we could compute the absolute dimensions of the or- 
bit described. Now Alpha Centauri and 61 Cygni are bot) 
binary stars, and their distances are tolerably well deter 
mined. It has been computed that the diameter of the orbL 
described by the components of Alpha Centauri is about 
four fifths that described by Uranus ; and that of 61 Cygni 
is considerably greater than the orbit of Neptune. 



THE FIXED STARS. 231 

419. Mass of a Binary Star computed. — Since the rela- 
tion between the dimensions of the orbit and the time of 
revolution determines the relative masses of the central 
bodies, we are able to compare the mass of a binary star 
with that of our sun when we know the periodic time of the 
star and the absolute radius of the orbit. We thus find 
that the mass of the double star Alpha Centauri is three 
fifths that of our sun ; that of 61 Cygni is about two thirds 
of our sun ; and that of the double star 10 Ophiuchi is three 
times that of our sun. 

420. The Fixed Stars are Suns. — We thus see that the 
fixed stars possess the same property of attraction that be- 
longs to the sun and planets. Some of them have a power 
of attraction nearly equal to that of our sun, and others 
have a greater power of attraction. Some of them emit 
more light than our sun. The fixed stars are therefore ma- 
terial bodies of vast size, and self-luminous, and are properly 
called suns. In the binary stars, then, we have examples, 
not of planets revolving round a sun, as in our solar system, 
but of one sun revolving around another sun; or, rather, 
of both around their common centre of gravity. 

421. Non-luminous Stars. — There is no evidence that all 
the stars emit light of equal intensity, and the great ine- 
quality in the components of some of the binary stars fa- 
vors the contrary supposition. Indeed, it has been surmised 
that some of the faint companions of double stars shine en- 
tirely by light reflected from the brighter star. This may 
perhaps be true of the companion of Sirius. 

The proper motion of some of the stars exhibits inequali- 
ties which have not been satisfactorily explained; and it 
has been conjectured that around these stars there may re- 
volve other bodies of a size sufficient to disturb their move- 
ments appreciably, but emitting a light so feeble that they 
can not be discerned with our telescopes. There is, then, 
some reason for supposing that there are stars which emit 
light of very feeble intensity, and perhaps others which are 
entirely non-luminous. Our sun is constantly emitting both 
heat and light, and, unless there is some provision which is 




232 ASTRONOMY. 

unknown to us for renewing the supply, our sun must ulti- 
mately become a non-luminous body. 

Fig . m 422. Multiple Stars. — Besides the 

binary stars, there are some triple 
stars which are proved to be physical- 
ly connected. There are also quadru- 
ple stars in which all the components 
are believed to be physically connect- 
ed, but the motion is so slow that it 
requires a longer period of observa- 
tions to show the connection indisput- 
ably. There are also quintuple and 
sextuple stars which are presumed to be physically con- 
nected. Fig. 122 shows the multiple star e Lyne. 

423. Clusters of Stars. — In many parts of the heavens Ave 
find stars crowded together into clusters, frequently in such 
numbers as to defy all attempts to count them. Some of 
these clusters are visible to the naked eye. In the cluster 
called the Pleiades, six stars are readily perceived by the 
naked eye, and Ave obtain glimpses of many more. With a 
telescope of moderate power 188 stars can be counted. 

In the constellation Cancer is a luminous spot called Prce- 
sepe, or the Bee-hive, which a telescope of moderate power 
resolves entirely into stars. In the sword-handle of Perseus 
is another luminous spot thickly crowded with stars, which 
are separately visible with a common opera-glass. 

One of the most magnificent clusters in the northern hem- 
isphere occurs in the constellation Hercules. On clear nights 
it is visible to the naked eye as a hazy mass of light, which 
is readily resolved into stars with a telescope of moderate 
power. When examined with a powerful telescope, it pre- 
sents the magnificent aspect of a countless host of stars 
crowded together into a perfect blaze of light. 

The richest cluster in the entire heavens is seen in the 
constellation Centaurus, in the southern hemisphere. To 
the naked eye it appears like a nebulous or hazy star of the 
fourth magnitude, while a large telescope shows it to cover 
a space having two thirds of the apparent diameter of the 



THE FIXED STARS. 233 

moon, and to be composed of innumerable stars apparently 
almost in contact with each other. 

Fig. 123. 




We can not doubt that most of the stars in this cluster 
are near enough to each other to feel each other's attraction. 
They must therefore be in motion, and we must regard this 
cluster as a magnificent astral system, consisting of a count- 
less number of suns, each revolving in an orbit about the 
common centre of gravity. 

424. Nebulae. — With the aid of the telescope we discern, 
scattered here and there over the firmament, dim patches 
of light, presenting a hazy or cloud-like appearance. These 
objects are called nebulce. With one or two exceptions, 
these objects can not be seen without a telescope, and many 
of them are beyond the reach of any but the most powerful 
instruments. 

The number of nebulae and clusters of stars hitherto dis- 
covered is somewhat over 5000. They are very unequally 
distributed over the heavens, being most numerous in the 
constellations Leo, Virgo, and Ursa Major, while in some 
other constellations very few are found. 



234 



ASTRONOMY. 



425. Diversity of Form and Appearance, — When viewed 
with telescopes of moderate power, most of the nebulae ap- 
pear round or oval, brighter toward their centres than at 
their borders. When examined with more powerful instru- 
ments, some of them are found to consist of a multitude of 
minute stars distinctly separate, without any remaining 
trace of nebulosity. About one twelfth of the whole num- 
ber have thus been entirely resolved into clusters of stars. 
Many others present a mottled, glittering aspect, abounding 
with stars, but mingled with a nebulosity which has not 
hitherto been resolved into stars. Others present no ap- 
pearance of stars, and retain the same cloud-like aspect un- 
der the highest power of the telescope. 

426. Classification of Nebulae. — The nebulae are some- 
times classified according to their forms as seen through the 
best telescopes. The following are the principal classes : 

1. Spherical or Spheroidal Nebula?. 

2. Annular or Perforated Nebulae. 

3. Spiral Nebulae. 

4. Planetary Nebulae. 

5. Stellar Nebulae. 

6. Irregular Nebula?. 

7. Double and Multiple Nebulae. 



427. Spherical or Spheroidal Nebulx. — Nebulae of a spher- 
ical form are very common. Many of them have a spher- 
oidal form; others are very much elongated; and some are 
so elongated as to be reduced almost to a straight line. 
They are generally most condensed toward the centre, and 
gradually fade away toward the margin. 

Fie. 124. Fig. 125. Fig. 126. 




THE FIXED STARS. 



23£ 



Fiff. 127. 



428, Annular or Perfo- 
rated Kebuhv. — There are 
only four examples of an- 
nular nebulae. Of these the 
most remarkable is that in 
Lyra, represented in Fig. 
12 7. In Lord Rosse's tel- 
escope are seen fringes ex- 
tending from each side of 
the ring, and also stripes 
crossing the central part. 



429. Spiral Nebulm.— Some of the nebulae exhibit spiral 
convolutions proceeding from a common nucleus or from 
two nuclei. The most remarkable example of this form is 
situated near the extremity of the tail of the Great Bear. 

Fig. 128. 





About forty spiral nebulae have been discovered, and there 
are others which exhibit some trace of this form. 



430. Planetary Nebulm. — Planetary nebulae have a round 
disc like a planet, exhibiting throughout a nearly uniform 
brightness, or only slightly mottled, and often very sharply 
defined at the margin. About twenty planetary nebulae 
have been observed. They can not be globular clusters of 
stars, otherwise they would appear brighter in the middle 
than at the borders. It has been conjectured that they are 
assemblages of stars in the form of hollow spherical shells, 



236 



ASTRONOMY. 



or of flat circular discs, whose planes are nearly at right an- 
gles to our line of vision. 

Fig. 129. Fig. 130 





431. Stellar Nebulae-. — Stellar nebulae are those in which 
one or more stars appear connected with a nebulosity. 
Sometimes we find a circular nebula with a star occupying 
the centre ; sometimes we find an elliptic nebula with a star 
at each focus ; sometimes we find a very elongated nebula 
with a star at each extremity of the major axis. 

432. Irregular Nebulae. — Most of the nebulae have no sim- 
ple geometrical form, and many of them exhibit remarkable 
irregularities, indicating an exceedingly complex structure. 
Of these, one of the most celebrated is the great nebula of 
Orion. It consists of irregular nebulous patches, whose ap- 
parent magnitude is more than twice that of the moon's 
disc. The brightest portion of the nebula resembles the 
head of a fish. It has been conjectured that this nebula has 
changed its form within two hundred years. 

Other celebrated nebulae which must be referred to this 
class are the great nebula in Andromeda (Fig. 131), the 



Fig. 131. 




THE FIXED STARS. 237 

Crab Nebula, the Dumb-bell Nebula (Fig. 132), etc., which 



Fig. 132. 



Fig. 133 





have been carefully delineated by Lord Rosse and other 
observers. 

433. Double and Multiple JSfebulce. — Some nebulae exhibit 
two centres of condensation. Sometimes the two portions 
are quite separate from each other, and sometimes they ap- 
pear to penetrate each other. Sometimes we find three, 
four, or more centres of condensation. It seems probable 
that the component parts of most of these nebulae are phys- 
ically connected. More than 50 double nebulae have been 
observed whose components are not more than five minutes 
apart. See Fig. 133. 

434. Magnitude of the Nebulce. — If we knew the distance 
of a nebula from the earth, we could deduce its absolute 
dimensions from its apparent diameter. We do not know 
the distance of any of the nebulae, but it is probable that 
their distance is as great as that of the faint stars into which 
some of them are partially resolved by the best telescopes. 

One of the planetary nebulae has an apparent diameter of 
about 3', the nebula of Orion has a diameter of 40', and that 
in Andromeda 90'. Even supposing these bodies to be re- 
moved from us no farther than 61 Cygni, the absolute diam- 
eter of the planetary nebula would be 7 times that of the 
orbit of Neptune, the nebula of Orion would be more than 
100 times, and that of Andromeda nearly 300 times the di- 
ameter of the orbit of Neptune. If, however, we suppose 



238 ASTRONOMY. 

them to be situated at the same distance as the faint stars 
into which they have been partially resolved, their absolute 
diameters would be 500 times greater than the numbers here 
stated. 

435. Variations in the Brightness of Nebulae. — Some of 
the nebulas are subject to variations of brightness. A neb- 
ula in Taurus, at the date of its discovery in 1852, was easi- 
ly seen with a good telescope, whereas in 1862 it w r as invis- 
ible with instruments of far greater power. A small star 
close to this nebula has also experienced a similar diminu- 
tion of brightness. Another nebula, situated near the Ple- 
iades, could be seen with a three-inch telescope in 1859, 
whereas in 1862 it could only be seen with difficulty through 
the largest telescope. Five or six cases of this kind have 
been noticed. It is probable that these variations of bright- 
ness are due to the same causes as the changes of the varia- 
ble stars. 

&Q6tT r ariatio?is in the Forms of Nebulce. — The forms of 
many of the nebulae are so peculiar that it is difficult to re- 
gard them as having attained a condition of permanent equi- 
librium, and it has been supposed that we now see them in 
the state of transition toward stable forms. A comparison 
of the present appearance of many nebulas with the repre- 
sentations of them furnished by former astronomers would 
lead to the conclusion that they had sensibly changed their 
form w T ithin 100 years, but this conclusion is rendered doubt- 
ful by the apparent imperfection of the earlier representa- 
tions. It is probable that future astronomers will discover 
decided changes in many of the nebulas. 

437. Are all Nebula?, resolvable into Stars? — Clusters of 
stars exhibit every gradation of closeness, from the Pleiades 
down to those which resemble the diffuse light of a comet. 
Many clusters, in which with ordinary telescopes the com- 
ponent stars are undistinguishable, when seen through more 
powerful telescopes are resolved wholly into masses of stars, 
so that some have concluded that all nebulas are but clus- 
ters of stars too remote for the individual stars to be sepa- 



THE FIXED STARS. 239 

rately seen. In other nebula?, the most powerful telescopes 
resolve certain portions into masses of stars, while other por- 
tions still retain the nebulous appearance. This result may 
sometimes be ascribed to difference of distance, while in 
other cases certain portions of the nebula? may consist of 
stars having actually a less magnitude, and crowded more 
closely together. Hitherto every increase of power of the 
telescope has augmented the number of nebula? which are 
resolved into clusters ; still it would be unsafe to infer that 
all nebulosity is but the glare of stars too remote to be sep- 
arated by the utmost power of our instruments. 

438. Spectra of the Nebulae-. — When the light of a fixed 
star is passed through a prism, its spectrum is generally con- 
tinuous from the red end to the violet, and is crossed by a 
system of dark lines, some of which correspond to lines in 
the solar spectrum. Some of the nebula?, as, for example, 
the great nebula in Andromeda, exhibit similar spectra. 
On the contrary, the spectra of some of the nebula? are not 
continuous, but their light is wholly concentrated into three 
bright lines, separated by obscure intervals. The great neb- 
ula in Orion, the Dumb-bell nebula, and the annular nebula 
in Lyra, furnish spectra of this kind. Such a spectrum is 
emitted when matter in the gaseous state is rendered lumin- 
ous by heat. The position of these bright lines indicates in 
these nebula? the presence of hydrogen and nitrogen, and a 
third element not yet identified. Hence it is inferred that 
these nebula? are not clusters of stars, but enormous masses 
of luminous gas. 

The nebulae may therefore be divided into two classes : 
1. Those whose spectra resemble the spectra of the fixed 
stars, and which are therefore regarded simply as clusters of 
stars; and, 2. Those whose spectra resemble that of lumin- 
ous gas. The latter are regarded, not as groups of stars, 
but true nebulw. None of the nebula? of this class have ever 
been resolved, although some exhibit a large number of 
minute stars, which, however, may be entirely distinct from 
the irresolvable matter of the nebula. 

A few of the fixed stars also exhibit a spectrum with 



240 ASTRONOMY. 

bright lines, which is considered to indicate that they are 
surrounded by an envelope of luminous gas. 

439. Belt of the Milky Way.— The Galaxy, or Milky Way, 
is that whitish, luminous band of irregular form which, on a 
clear night, is seen stretching across the firmament from one 
side of the horizon to the other. The general course of the 
Milky Way is in a great circle, inclined about 63° to the 
celestial equator, and intersecting it near the constellations 
Orion and Ophiuchus. It varies in breadth at different 
points from 5° to 16°, having an average breadth of about 
10°. To the naked eye it presents a succession of luminous 
patches, unequally condensed, intermingled with others of a 
fainter shade. From Cygnus to Scorpio it divides into two 
irregular streams, which in some places expand to a breadth 
of 22°. 

When examined in a powerful telescope, the Milky Way 
is found to consist of myriads of stars, so small that no one 
of them singly produces a sensible impression on the unas- 
sisted eye. These stars are, however, very unequally dis- 
tributed. In some regions several thousands are crowded 
together within the space of one square degree ; in others, 
only a few glittering points are scattered upon the black 
ground of the heavens. 

440. Hypothesis of Sir William Herschel. — Herschel at- 
tempted to explain the great accumulation of stars near the 
plane of the Milky Way by supposing that the stars of our 
firmament constitute a cluster with definite boundaries, the 
thickness of the cluster being small in comparison with its 
length and breadth, and the earth occupying a position 
somewhere about the middle of its thickness. If we sup- 
pose the stars to be scattered pretty uniformly through 
space, the number of the stars visible in the field of a tele- 
scope ought to be about the same in every direction, pro- 
vided the stars extend in all directions to an equal distance. 
But if the stars about us form a cluster whose thickness is 
less than its length and breadth, then the number of stars 
visible in different directions will show both the exterior 
form of the cluster and the place occupied by the observer. 



THE FIXED STARS. 241 

441. Her scheV s Hypothesis is untenable. — This hypothesis 
assumes that the stars are distributed uniformly through 
space, and that Herschel's telescope penetrated to the out- 
ermost limits of our cluster. The first assumption is not 
true, for the stars are greatly condensed in the neighbor- 
hood of the plane of the Milky Way. The second assump- 
tion must also be abandoned, for every increase in the power 
of our telescopes discloses new stars which before have been 
invisible. We conclude, therefore, that the cluster of stars 
composing the Milky Way extends in all directions beyond 
the reach of the most powerful telescopes, and we have no 
knowledge of the exterior form of the cluster. 

442. Madler* s Hypothesis respecting the Milky Way. — 
Madler supposes that the stars of the Milky Way are 
grouped together in the form of an immense ring, or sev- 
eral concentric star rings of unequal thickness and various 
dimensions, but all situated nearly in the same plane. To 
an observer situated in the centre of such a system of rings, 
the inner ring would seem to cover the exterior ones ; that 
is, the stars would seem to form but a single ring, and this 
ring would be a great circle of the sphere. The division 
of the Milky Way throughout a considerable portion of its 
extent into two separate branches indicates that in this part 
of the firmament the star rings do not cover each other, 
which Madler explains by supposing that we are situated 
nearer to the southern than the northern side of the rings. 

443. Primitive Condition of the Solar System. — We ob- 
serve in our solar system several remarkable coincidences 
which we can not well suppose to be fortuitous, and which 
indicate a common origin of the system of planets circulat- 
ing around the sun. 

1. All the planets revolve about the sun in the same di- 
rection, viz., from west to east. 

2. Their orbits all lie nearly in the same plane, viz., the 
plane of the sun's equator. 

3. The sun rotates on an axis in the same direction as that 
in which the planets revolve around him. 

4. The satellites (as far as known) revolve around their pri- 

L 



242 ASTRONOMY. 

maries in the same direction in which the latter turn on their 
axes, and nearly in the plane of the equator of the primary. 

5. The orbits of all the larger planets and their satellites 
have small eccentricity. 

6. The planets, upon the whole, increase in density as they 
are found nearer the sun. 

7. The orbits of the comets have usually great eccentrici- 
ty, and have every variety of inclination to the ecliptic. 

These coincidences are not a consequence of the law of 
universal gravitation, yet it is highly improbable that they 
were the result of chance. They seem rather to indicate 
the operation of some grand and comprehensive law. Can 
we discover any law from which these coincidences would 
necessarily result ? 

444. Conclusions from Geological Phenomena.- — An ex- 
amination of the condition and structure of the earth has 
led geologists to conclude that our entire globe was once 
liquid from heat, and that it has gradually cooled upon its 
surface, while a large portion of the interior still retains 
much of its primitive heat. The shape of the mountains in 
the moon seems to indicate that that body was formerly in 
a state of fusion. But if the earth and moon were ever sub- 
jected to such a heat, it is probable that the other bodies 
of the solar system were in a like condition, perhaps at a 
temperature sufficient to volatilize every solid and liquid 
body, constituting perhaps a single nebulous mass of very 
small density. 

445. The Nebular Hypothesis. — Let us suppose, then, 
that the matter composing the entire solar system once ex- 
isted in the condition of a single nebulous mass, extending 
beyond the orbit of the most remote planet. Suppose that 
this nebula lias a slow rotation upon an axis, and that by 
radiation it gradually cools, thereby contracting in its di- 
mensions. This contraction necessarily accelerates tne ve- 
locity of rotation, and augments the centrifugal force, and 
ultimately the centrifugal force of the exterior portion oi 
the nebula would become equal to the attraction of the cen 
tral mass,, 



THE FIXED STARS. 243 

This exterior portion would thus become detached, and 
revolve independently of the interior mass as an immense 
nebulous zone or ring. As the central mass continued to 
cool and contract in its dimensions, other zones would in 
the same manner become detached, while the central mass 
continually decreases in size and increases in density. 

The zones, thus successively detached, would generally 
breakup into separate masses, revolving independently about 
the sun ; and if their velocities were slightly unequal, the 
matter of each zone would ultimately collect in a single 
planetary but still gaseous mass, having a spheroidal form, 
and also a motion of rotation about an axis. 

As each of these planetary masses became still farther 
cooled, it would pass through a succession of changes simi- 
lar to those of the first solar nebula ; rings of matter would 
be formed surrounding the planetary nucleus, and these 
rings, if they broke up into separate masses, would ultimate- 
ly form satellites revolving about their primaries. 

446, Phenomena explained by this Hypothesis. — The first 
six of the phenomena mentioned in Art. 443 are obvious 
consequences of this theory. The eccentricty of some of 
the planetary orbits and their inclination to the sun's equa- 
tor may be explained by the accumulated effect of the dis- 
turbing action of the planets upon each other, 

The pianet Saturn presents the only instance in the solar 
system in which the detached nebulous zone condensed 
uniformly, and preserved its unbroken form. The group of 
small planets between Mars and Jupiter presents an instance 
m wnich a ring broke up into a great number of small 
fragments, which continued to revolve in independent orbits 
about the sum 

447. Apparent Anomalies explained. — The satellites of 
Uranus and Neptune form an exception to the general 
movement of the planets and their satellites from west to 
east, and this fact has been supposed to be inconsistent with 
the nebular hypothesis. There is, however, no such incon- 
sistency. Planets formed in the manner here supposed 
would all have a movement of rotation, but they would not 



244 ASTRONOMY. 

necessarily rotate in the same direction as the motion of 
revolution. The outer planets might rotate in the contrary 
direction, but in all cases the satellites must revolve in their 
orbits in the same direction as the rotation of the primary. 
If it shall be discovered that the planets Uranus and Nep- 
tune rotate upon their axes in a direction corresponding 
with the revolution of their satellites, these movements 
would be consistent with the nebular hypothesis. 

The fact that cometary orbits exhibit every variety of 
inclination to the ecliptic has also been supposed to be in- 
consistent with the nebular hypothesis. The comets of 
short period move in orbits which differ but little from those 
of the minor planets, and we may suppose them to consist 
of small portions of nebulous matter which became detached 
in the breaking up of the planetary rings, and continued to 
revolve independently about the sun. 

The comets which travel beyond the limits of the solar 
system probably consist of nebulous matter encountered by 
the solar system in its motion through space, and thus 
brought within the attractive influence of the sun. They 
are thus compelled to move in orbits around the sun, and 
these orbits may sometimes be so modified by the attraction 
of the planets that they may become permanent members 
of our solar system. 

448. How the Nebular Hypothesis may be tested. — This 
hypothesis may be tested in the following manner. The 
time of revolution of each of the planets ought to be equal 
to the time of rotation of the solar mass at the period when 
its surface extended to the given planet. Let us, then, sup- 
pose the sun's mass to be expanded until its surface extends 
to the orbit of Mercury. If we compute the time of rota- 
tion of this expanded solar mass, we shall find it to be near- 
ly four months, which corresponds with the time of revolu- 
tion of Mercury. If we suppose the sun's mass to be farther 
expanded until its surface extends to each of the planets in 
succession, we shall find by computation that the time of ro- 
tation of the expanded solar mass is very nearly equal to 
the actual time of revolution of the corresponding planet. 

So, also, if we suppose the earth to be expanded until its 



THE FIXED STARS. 245 

surface extends to the moon, we shall find by computation 
that its time of rotation corresponds nearly with the time 
of revolution of the moon. In like manner, if Ave suppose 
each of the primary planets to be expanded until its surface 
extends to each of its satellites in succession, we shall find 
that its computed time of rotation is very nearly equal to 
the actual time of revolution of the corresponding satellite. 
The nebular hypothesis must therefore be regarded as 
possessing a high degree of probability, since it accounts for 
a large number of phenomena which hitherto had remained 
unexplained. 



TABLE I. — ELEMENTS OF THE PRINCIPAL PLANETS. 



r 

Name. 


Mean Distance from the Sun. 


Eccentricity. 


1 


Relative. 


In Miles. 


i , Mercury 


O.38710 
0. 72333 
I .OOOOO 
I . 52369 
5.2028o 

9.53885 
19. 18264 
3o. 03697 


3?^552,ooo 

66,43i,ooo 

91,841,000 

139,937,000 

477,83i,ooo 

876,058,000 

1,761,763,000 

2,758,566,000 


0.20562 

.oo683 
.01677 
.09326 
.04824 
.o56oo 
.04658 
.00872 


Venus 


Earth 


Mars 


Jupiter 


Saturn 


Uranus 


Neptune 





Name. 


Sidereal 

Period 

in Years. 


Synodic;'.l 

Period 
in Days. 


Equatorial 
Diameter 
in Miles. 


Mass. 


Mercurv 


0.24o 

o.6i5 
1 .000 

1.880 
11.862 
29.458 
84.018 

164.622 


115.877 
583.921 

77 9 . 9 36 
3 9 8.884 
378.092 

36 9 .656 

367.489 


3,067 

7,814 

7,926 
4, 5oo 
87,890 
74,327 
33,200 
36,ioo 


O. Il8 

o.883 
1 .000 

O. l32 

338.o34 
101 .064 

i4-7 8 9 
24-648 


Venus 


Earth 


Mars 


j Jupiter 


' Saturn , 


1 Uranus 


Neptune 





248 



TABLE II. — THE MINOR PLANETS. 



No. 


Planet's Name. 


Date of Discovery. 


Mean 
Distance. 


Sidereal 

Period 

in Days. 


Eccen- 
tricity. 


Diame- . 
ter in 
Miles. 


I 


Ceres 


1801, Jan. 1 


2.770 


1684 


O.080 


227 


2 


Pallas 


1802, March 28 


2 . 770 


i683 


.24o 


172 


3 


Juno 


1804, Sept. 1 


2.667 


1591 


.258 


112 


4 


Vesta 


1807, March 29 


2. 36i 


i325 


.090 


228 


5 


Astraea 


i845, Dec. 8 


2.5 77 


i5n 


. 190 


6l 


6 


Hebe 


1847, July 1 


2.426 


i38o 


.202 


IOO 


7 


Iris 


1847, Aug. 1 3 


2.386 


1 346 


.231 


96 


8 


Flora 


1847, Oct. 18 


2.201 


1193 


.i5 7 


60 


9 


Metis 


1848, April 25 


2.386 


1 346 


. 123 


76 


IO 


Hygcia 


1849, April 12 


3.i54 


2046 


. io5 


II I 


ii 


Parthenope 


i85o, May 11 


2.453 


i4o3 


.099 


62 


12 


Victoria 


i85o, Sept. 1 3 


2.334 


i3o3 


.219 


4i 


i3 


Egeria 


i85o, Nov. 2 


2 . 576 


i5io 


.087 


73 


i4 


Irene 


i85i, May 19 


2.589 


l522 


.i65 


68 


i5 


Eunomia 


1 85 1, July 29 


2.643 


1570 


. 187 


92 


16 


Psyche 


1 852, March 17 


2 .921 


1824 


.i36 


9 3 


17 


Thetis 


1 852, April 17 


2.473 


1421 


. 127 


52 


18 


Melpomene 


1 852, June 24 


2.296 


1270 


.218 


54 


1 I9 


Fortuna 


i852, Aug. 22 


2.441 


i3 9 3 


.i5 7 


61 


1 20 


Massilia 


i852, Sept. 19 


2.409 


i365 


• i44 


68 


) 21 


Lutetia 


i852, Nov. i5 


2.435 


i388 


. 162 


4o 


22 


Calliope 


1 852, Nov. 16 


2.91 1 


1814 


.099 


96 


23 


Thalia 


1 852, Dec. 1 5 


2.63i 


i558 


.232 


42 


24 


Themis 


1 853, April 5 


3. 139 


203l 


.117 


36 


25 


Phocasa 


1 853, April 7 


2 .401 


i35 9 


.255 


3i 


26 


Proserpine 


1 853, May 5 


2.656 


i58i 


.087 


47 


27 


Euterpe 


1 85 3, Nov. 8 


2.347 


i3i3 


.i 7 3 


39 


28 


Bellona 


1 854, March 1 


2.778 


1692 


. i5o 


5 9 


29 


Amphitrite 


1 854, March I 


2.554 


1491 


.074 


83 


3o 


Urania 


1 854, July 22 


2.367 


i33o 


. 127 


5i 


3i 


Euphrosyne 


1 854, Sept. 1 


3.i5i 


2045 


.221 


5o 


32 


Pomona 


1 854, Oct. 26 


2.58 7 


1520 


.082 


35 


33 


Polyhymnia 


1 854, Oct. 28 


2.865 


1771 


.33 9 


38 


34 


Circe 


1 855, April 6 


2.687 


1609 


. 107 


29 


35 


Leucothea 


1 855, April 19 


2. 99 3 


1891 


.214 


25 


36 


Atalanta 


i855, Oct. 5 


2. 745 


1661 


.302 


20 


37 


Fides 


i855, Oct. 5 


2. 64 1 


i568 


.177 


4i 


38 


Led a 


1 856, Jan. 12 


2.740 


i65 7 


.i55 


29 


3 9 


Lsetitia 


i856,Feb. 8 


2.764 


1680 


.111 


87 


4o 


Harmonia 


1 856, March 3i 


2 .267 


1247 


.046 


61 



TABLE II. THE MIX OK PLAXETS. 



249 









Mean 
Distance. 


Sidereal 




Diame- 


No. 


Planet's Name. 


Date of Discovery. 


Period 
in Pays. 


Eccen- 
tricity. 


ter in 


4i 


Daphne 


I $56, May 22 


2.758 


l6 7 3 


. 270 


61 


42 


Isis 


1 856, May 2 3 


2.44o 


l392 


.226 


3 9 


43 


Ariadne 


1857, April 1 5 


2.203 


1194 


. 167 


33 


44 


Nisa 


1857, May 27 


2.422 


i3 77 


.i5i 


42 


45 


Eugenia 


1857, June 27 


2.72I 


1639 


.082 


44 


| 46 


Hestia 


1857, Aug. 16 


2.526 


i466 


.164 


25 


4? 


Aglaia 


1857, Sept. i5 


2.878 


1784 


.i34 


43 


48 


Doris 


1857. Sept. 19 


3.108 


2001 


.076 


57 


49 


Pales 


1857, Sept. 19 


3.082 


1978 


.237 


61 


5o 


Virginia 


1857, Oct, 4 


2 .652 


1077 


.284 


25 


5i 


Nemausa 


i858, Jan. 22 


2.366 


i3s8 


.068 


38 


52 


Europa 


i858,Eeb. 6 


3. 107 


2000 


. 101 


72 


53 


Calypso 


1 858, April 4 


2 .621 


i55o 


.203 


29 


54 


Alexandra 


i858, Sept. 10 


2 . 709 


1629 


.199 


4o 


55 


Pandora 


1 858, Sept. 10 


2.761 


1676 


.145 


44 


56 


Melete 


1857, Sept. 9 


2.597 


i528 


.236 


29 


5? 


Mnemosyne 


1859, Sept. 22 


3.i55 


2048 


. 109 


63 


58 


Concordia 


i860, March 24 


2 . 700 


1620 


.042 


3i 


5 9 


Elpis 


i860, Sept. 12 


2.713 


i632 


.117 


36 


6o 


Echo 


i860, Sept. 1 5 


2.3 9 3 


i352 


.i85 


17 


6i 


Danae 


i860, Sept. 19 


2.987 


i885 


.161 


38 


62 


Erato 


i860, Oct. 


3.i3i 


2023 


.170 


4o 


63 


Ausonia 


1 86 1, Feb. 10 


2.395 


i354 


. 125 


49 


64 


Angelina 


1 86 1, March 4 


2.681 


i6o3 


.128 


44 


65 


Cybele 


1 86 1, March 8 


3.420 


23ll 


. 120 


63 


66 


Maia 


1 86 1, April 9 


2.65i 


i5 77 


.i58 


18 


67 


Asia 


1 86 1, April 17 


2.422 


i3 7 6 


.i85 


22 


68 


Leto 


1 86 1, April 29 


2.781 


1695 


.188 


60 


69 


Hesperia 


1 86 1, April 20 


2. 97 5 


i8 7 3 


. 172 


32 


70 


Panopsea 


1 86 1, May 5 ' 


2.6i3 


1 543 


.184 


36 


7i 


Niobe 


1 86 1, May 29 


2.754 


1670 


.i 7 4 


46 


72 


Feronia 


1 86 1, Aug. 1 3 


2.266 


1245 


. 120 




73 


Clytia 


1862, April 7 


2.665 


i58 9 


.o44 




74 


Galatea 


1862, Aug. 29 


2.780 


1693 


.237 




75 


Eurydice 


1862, Sept. 22 


2 .670 


1594 


.307 




76 


Freia 


1862, Oct. 21 


3.388 


2277 


.188 




77 


Erigga 


1862, Nov. 12 


2.674 


1596 


.i36 




78 


Diana 


1 863, March i5 


2.623 


i552 


.206 




79 


Eurynome 


i863, Sept. i4 


2.444 


1395 


. 193 




80 


Sappho 


1864, May 2 


2 .296 


1270 


.200 





L 2 



250 



TABLE II. THE MINOR PLANETS. 



1 No. 

j 


Planet's Name. 


Date of Discovery. 


Mean 
Distance. 


Sidereal 

Period 

in Days. 


Eccen- 
tricity. 


Diame- 
ter in 

Miles. 


! 81 


Terpsichore 


1864, Sept. 3o 


2.854 


1761 


0.21 1 




| §2 


Alcmene 


1864, Nov. 27 


2. 760 


1674 


.226 




83 


Beatrix 


1 865, April 26 


2.43i 


1 384 


.086 




84 


Clio 


i865, Aug. 25 


5.362 


i325 


.236 




85 


Io 


1 865, Sept. 19 


2,654 


1579 


.191 




86 


Semele 


1866, Jan. 4 


3. 112 


2005 


.2IO 




87 


Sylvia 


1866, May 16 


2.494 


2 385 


.082 




88 


Thisbe 


1866, June 1 5 


2,769 


1682 


.i65 




89 


Julia 


1866, Aug. 6 


2.55o 


i486 


.180 




90 


Antiope 


1866, Oct. 1 


3.i37 


2029 


.i 7 3 




9 1 


JEgina 


1866, Nov. 4 


2.492 


i43 7 


.066 




92 


Undina 


1867, July 7 


3. 192 


2 o83 


. io3 




9 3 


Minerva 


1867, Aug. 24 


2.756 


1671 


. i4o 




94 


Aurora 


1867, Sept. 6 


3. 160 


2052 


.089 




9 5 


Arethusa 


1867, Nov. 2 3 


3.069 


1964 


.146 




9 6 


JEgle 


1868, Feb. 17 


3.o54 


1950 


. i4o 




97 


Clotho 


1868, Feb. 17 


2.669 


l592 


.257 




98 Ian the 


1868, April 18 


2.685 


i6o3 


.189 




99 


Atrophos 


1868, May 29 


2.797 


1708 


.238 




100 


Hecate 


1868, July 11 


3.098 


1992 


.i56 




101 


Helena 


1868, Aug. i5 


2.584 


i5i8 


. 139 




102 


Miriam 


1868, Aug. 22 


2.661 


1 586 


.255 




io3 


Hera 


1868, Sept. 7 


2 . 702 


1622 


.084 




io4 


Clymene 


1868, Sept. 1 3 


3.i5i 


2o43 


.177 




io5 


Artemis 


1868, Sept. 16 


2.376 


i338 


.i 7 3 




106 


Dione 


1868, Oct. 10 


3. 160 


2052 


.i83 




107 


Camilla 


1868, Nov. 17 


3.56o 


2454 


.123 




108 


Hecuba 


1869, April 2 


3.211 


2102 


. 100 




109 


Felicitas 


1869, Oct. 9 


2 .695 


l6l6 


.299 




no 


Lydia 


1870, April 19 


2 . 740 


i65 7 


.080 




1 1 1 


Ate 


1870, Aug. i4 


2.594 


i526 


. 106 




I 12 


Iphigenia 


1870, Sept. 19 


2.433 


i386 


. 129 




n3 


Amalthea 


1 87 1, March 12 


2.376 


i338 


.088 




n4 


Cassandra 


1 87 1, July 2 3 


2.676 


i5 99 


. i4o 




n5 


Thyra 


1 87 1, Aug. 6 


2.3 79 


1 34o 


.194 




116 


Sirona 


1871, Sept. 8 


2 . 766 


1680 


.i44 




117 


Lorn i a 


1871, Sept. 12 


2.991 


1889 


.023 




118 


Peitho 


1872, March i5 


2.438 


1390 


.i65 




119 


Althea 


1872, April 3 


2.58o 


i5i4 


.084 




120 


Lachesis 


1872, April 10 


3.i32 


2025 


.o54 





INDEX. 



Aberration, amount of 

" illustrated 

" of a star at the pole 

Aerolites described 

11 orbits of 

" origin of 

Altitude and^azimuth defined 

" and azimuth instrument. .. 

" of a body determined 

Aitirudes measured by sextant 

Annual parallax of stars 

Annular mountains of moon 

Apparent motion of inferior planet. . . 

M " of superior planet.. 

Arc of meridian, how measured 

Asteroid system, origin of. > 

Asteroids, brightness of. 

" distance of 

" number known 

Astronomy defined 

Atmosphere, illuminating effect of. . . 
Atmospheric refraction, law of 

Biela's comet divided 

" " history - 

Binary star, mass of. 

Binary stars defined 

" " elements of 

" " number of 

Brorsen's comet 

Calendar, Gregorian 

" Julian 

Cavendish's experiment 

Celestial equator defined 

" globe, problems on 

" sphere defined 

" " time of revolution. .. 

Centrifugal force, and force of gravity 

" " and form of body.. 

" " effects of. 

Change of seasons, cause of 

" " made greater 

Chronometers, longitude by 

Clock, its error and rate 

Clusters of stars 

Color of the stars 

Colures, equinoctial and solstitial 

Coma, nucleus, etc., of comet 

Cometary orbits, nature of. 

" " position of 

Comet defined 

" known to be periodic 

" of 1744, history 

" of 1770, history 

" of 1770, mass of 

" of 1S43, history 

" strike the earth. 



Page) 

102 Comet's tail, dimensions of 

101 " " formation of 

102 " " position of 

211 1 " tails, theory of 

218 Comets, number of 

213 

13 
51 
50 
53 
222 



period of visibility 

phases of 

quantity of matter 

telescopic 

variations of 

with several tails 

US Cone of earth's shadow 

156 Conic sections, planets move in 

15S Conjunction and opposition defined.. 



et.. 



of a plan- 



Constellations enumerated 

" names of. 

" origin of. 

9 Constitution of the sun 

61 Corona in solar eclipses 

55Cotidal lines 

| Culminations of heavenly bodies 

203 Curvilinear motion 

202| 

231 D'Arrest's comet 

229 Day, civil and astronomical 

230 Decimation defined 

230 " how determined 

204 Density of earth determined 

" of a planet determined 

79 Detonating meteors described 

79 " " velocity 

33 Differences of parallax detected 

12 Dip of the horizon 

S6 Direction of sun's motion 

10 Distance between two stars computed 

11 " measured by sextant 

27 " of a planet from sun 

27 *• of heavenly body computed. 

26 " of the sun computed 

06 Diurnal inequality in North Atlantic. 
68 " " in Pacific 

140 1 " " variations of 

41 Diurnal motion, cause of 

232 " " consequences of. 

223 " " described 

63 " " never suspended 

190 " " rate of 

19S Diurnal paths of heavenly bodies — 

189 Donati's comet 

1S9 Double stars classified 

199 •« " defined 

205 

205 Earth, circumference of 

206 " dimensions of, important 

206 " ellipticity of. 

2071 " form and dimensions 



Paw 

194 

193 
194 
195 
1S9 
190 
197 
197 
197 
192 
196 
129 
126 
107 

155 

218 
217 
217 

97 
136 
148 

11 
121 

204 

73 

24 

50 

32 

164 

210 

211 

223 

53 

226 

230 

53 

162 

82 

S9 

151 

151 

152 

20 

13 

9 

11 

46 

11 

207 

228 

227 

19 
15 
31 
3d 



252 



INDEX. 



Page 

Earth, proof that it is globular. ...... 10 

Earth's annual motion, effects of 66 

" atmosphere, effect of. 132 

" axis defined 21 

" diameter, how determined. .. 17 

" motion in its orbit 71 

M " velocity of 

" orbit an ellipse C9 

" " eccentricity of 69 

" " form of. 69 

" penumbra defined 131 

' " rotation, direct proof of 35 

" shadow, breadth of. 130 

" " form of 129 

" " length of 130 

* surface, irregularities of 19 

Eclipse of snn, darkness of 136 

Eclipses, cause of , 129 

** every month 129 

" number in a year 136 

" of Jupiter's satellites 178 

11 of sun and moon compared. 136 

" of sun, different kinds 135 

" " duration of. 135 

Ecliptic, position of 103 

Electric circuit broken by clock 143 

Electro-chronograph 45 

Encke's comet, history 201 

" hypothesis considered 201 

Enlargement of sun near horizon 53 

Equation of time : value of. 76 

Equatorial telescope defined. 10 

Equinoxes and solstices 63 

" precession of 10: 

Establishment of a port 153 

Faculse, cause of 92 

Falling bodies, experiments 37 

" " motion of 36 

Faye's comet, history 204 

Fixed star defined 215 

Fixed stars are suns 231 

" " classified 215 

Force that retains the moon 124 

Geocentric and heliocentric places. . . 155 

Geological phenomena 242 

Globe, celestial, problems 86 

" terrestrial, " 39,82 

Globes, artificial 37 

Gravitation proportional to masses.. 125 

Greatest heat after the solstice 70 

Gregorian Calendar adopted 80 

Halley's comet, history 199 

" " return..!. 201 

Harvest moon explained 112 

Herschel's hypothesis 240 

Horizon, seusible and rational 12 

Horizontal point determined 49 

Hour circles defined 23 



Jupiter's satellites, eclipses of 



Page 
. 178 



Inequality of solar days 74 

Jupiter, belts of 177 

11 diameter 176 

" distance and period 176 

" rotation of. 176 

11 spheroidal form 177 

Jupiter's belts explained 1771 

44 satellites, distances of 178lNcbula, dumb-bell 237 



Kepler's laws 121 

third law 128 

Latitude and longitude defined 21 

" " " of a star 65 

" at sea determined 72 

" of a place determined 71 

11 " " how known 23 

Law of gravitation general 124 

Le Verrier and Adams's researches . . 187 

Librations of the moon 113 

Light of sun and stars 224 

" transmission of ISO 

Longitude by artificial signals 140 

" " chronometers 140 

" " eclipses of moon... .. . . 141 

" " electric telegraph 142 

" " Jupiter's satellites 180 

" " solar eclipse 142 

Lunar eclipses, different kinds 131 

" mountains, height of 115 

" volcanoes extinct 120 

Madler's hypothesis 241 

Mars, color of 1T.% 

" distance and period 172 

" phases 172 

" spheroidal form 173 

" telescopic appearance 173 

Measurements of meridian arcs 29 

Mercury and Venus, elongations 165 

" " phases of 165 

" " transits of 169 

greatest brightness of. 167 

period and distance 166 

rotation on axis 167 

Mercury, visibility of. 166 

Meridian circle 50 

Meridian mark 77 

Meteoric orbits 203 

Meteors of August and November ... 209 

Milky way 240 

Moon, causes no refraction 116 

circular craters 118 

diameter of 107 

distance of 107 

revolution of 108 

rotation and revolution of 112 

telescopic appearance. 114 

visible in total eclipse 133 

Moon's atmosphere 116 

disc, obscure part Ill 

mountain forms « 117 

orbit, eccentricity of 109 

form of. 109 

phases 110 

rising, daily retardation. ...... M2 

rotation upon an axis 112 

shadow, breadth of 134 

" length of .. 133 

" velocity of. 134 

transits, interval of 109 

Motion, direct and retrograde 157 

of the solar system 226 

on a curve, law of. 122 

Multiple stars 232 

Mural circle described 47 



INDEX. 



253 



Nebula in Andromeda 

14 in Lyra 

" spiral 

Nebulae, changes of 

" classification of 

" described 

" planetary 

" resolvable into stars ..... 
spectra of 

11 spiral. « , 

" stellar 

Nebular hypothesis, argument for. 

11 " stated 

Nebulosity of comets 

Neptune discovered at Berlin 

" distance and period . 

" satellite of 

Nucleus of comet, dimensions of.. . 
Nutation, solar and lunar 



Oblique sphere defined 

Obliquity of ecliptic determined 

Observations for moon's parallax . . 

11 made in meridian. . . . 

Occultations of Jupiter's satellites . 

" of stars..., 

Olbers's hypothesis inadmissible, . . 

" " stated. .... 

Orbit of a binary star « 



Parallax, diurnal, explained 

" of Alpha Centauri , 

11 of moon determined. ..... 

11 ofGlCygni 

1 ' of various stars 

Parallel sphere defined. 

Periodicity, cause of 

Periodic time of a planet 

Planet, deficient 

" elements of orbit 

" phases of. 

" when visible 

Planets, apparent motion of. 

11 attractive force of 

" diameter of. 

" number of. 

H orbits of. 

" peculiarities of 

Pole, altitude of. 

" of equator, motion of. 

il star, how found 

11 " varies 

Precession of equinoxes, cause of . . 

Projectiles, motion of 

Proper motion of stars explained . . 
Protuberances emanate from sun . . 

" flame-like 

" nature of 



25 

OS 
82 
41 
171) 
139 
176 
174 
230 

80 
222 

81 
223 



Reading microscope described 

Refraction affected by temperature. . . 

" atmospheric 

" determined by observation 

Resisting medium 

Reticle of telescope 

Revolution of celestial sphere, time of 
Revolutions, sidereal and synodic. . . . 

Right ascension defined 

" sphere defined 



Satellites, number of 155 



Tape p apa 

236 Saturn, diameter of 181 

235 " distance and period of 181 

235 " rotation of 181 

238 Saturn's inner ring , 153 

234 " rings, appearance of lsi 

233 " " constitution of. 184 

235 " " dimensions of ls.3 

23S " " disappearance of. 183 

239 " " how sustained 184 

235 " " variations of. " 182 

236 " satellites *. 185 

243 Sextant described 52 

242 Shooting stars described 208 

191 " " height and velocity of. 208 

18] Sidereal and solar time compared 73 

188 " day defined n 

1SS " period, how determined 102 

191 " time defined 72 

105 Solar corona, cause of. \ 138 

faculse are elevations .......... 92 

spots, black nucleus 90 

" changes of. 91 

" depressions 95 

" described 90 

" latitude of. 95 

" magnitude of. 91 

' ' motion of 94 

" not planets 93 

" observations of 92 

11 origin of 98 

" penumbra of 98 

" periodicity of. 91 

system seen from Neptune 1SS 

time defined 72 

224jSpirit-level described 43 

25' Star Alpha Centauri 222 

221 Stars, brightness of 216 

catalogues of 220 

constitution of 225 

distance of 222 

how designated 218 

how visible 210 

nor-luminous 231 

optically double 229 

periodic 220 

proper motion of 225 

temporary 220 

which never set 15 

Sun- dial described 78 

Sun, diameter of 89 

Sun's disc affected by refraction 58 

" bright part of 92 

envelope not solid 96 

equator, position of 95 

force of gravity 90 

motion in declination 02 

" in right ascension 62 

" rectilinear 226 

parallax and distance 109 

11 determined 171 

* J from Mars 174 

photosphere, nature of 97 

rotation, time of 94 

Sunrise affected by refraction 58 

Superior planets distinguished 172 

Synodic period determined 108 

Tail of comet 193 

Tidal currents 151 

Tidal wave in shallow water 149 

" near South America 143 



161 

. 174 

. 160 

, 160 

159 

156 

124 

163 

154 

154 

160 

22 

103 

15 

104 

105 

127 

227 j 

137! 

137 

13S! 

49 
57 
55 
56 

201 
41 
11 

10S 
23 
24 



254 



INDEX. 



Page 

Tidal wave, origin of 148 

" " velocity of 14S 

Tides at perigee and apogee 145 

caused by the sun 147 

cause of 14G 

denned 145 

depend on moon's declination. 147 

diurnal inequality of 151 

height of 149 

how modified 150 

in Bay of Fimdy 150 

of coast of Europe 152 

of Gulf of Mexico 152 

of inland seas 152 

of rivers 150 

oZ the Pacific Ocean 151 

on coast of Europe 152 

spring and neap 145 

fvhy complicated 148 

ime, apparent and mean 73 

by a single altitude 78 

determined 76 

under different meridians 140 

Trau-nt instrument adjusted 46 

" " described. 42 

" verified 47 

Tran-iits. mod^ of observing 44 

" s>f Mercury, possible .- . 169 

*' vQf start telegraphed , . . 1M 

'* of V<?,nu% *)lise/ved . 17v 



I Pa S « 

Tropics and polar circles 64 

Twilight, cause of. 59 

" duration at equator .. , 60 

11 " at poles 60 

" " in middle latitudes 61 

Uranus, diameter of. 186 

" distance and period of. 186 

" satellites of 187 

Venus, morning star 168 

" period and distance of 167 

" rotation on axis of. 168 

" twilight of 16-3 

" visible in daytime 163 

Vernier described 48 

Vertical circle defined 12 

Volcanoes, lunar 118 

terrestrial 119 

Water on the moon 117 

Weight at pole and equator 27 

loss of, at equator 31 

Winnecke's comet 205 

Zenith and nadir defined 12 

Zodiacal light 99 

Zodiac, signs and constellations of. . . 105 

11 " enumerated 64 

Zones of the earth 65 



THE END. 



J °U 



°1948 



,^'BRARY OF CONGRESS 




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